Last updated: 1/27/2014
Niagara Falls City School District
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Mathematics - Grades 9-12 - Geometry (Regents) 2005 Edition 10, 20, 30, 40 Weeks

Holt Geometry
 (2) MST3.G.G.17 Students construct a bisector of a given angle, using a straightedge and compass, and justify the construction.
Chapter 1
Students construct a bisector of a given angle, using a straightedge and compass, and justify the construction.
1-3 Amsco A: 24-1, 24-2 Physics - pendulum
 (2) MST3.G.G.48 Students investigate, justify, and apply the Pythagorean theorem and its converse.
Students investigate, justify, and apply the Pythagorean theorem and its converse. 1-6 Amsco A: 16-10, 21-4 Global Studies - const. of Forbidden City in Beijing, China
 (3) MST3.G.G.66 Students find the midpoint of a line segment, given its endpoints.
Students find the midpoint of a line segment, given its endpoints. 1-6 Amsco A: 10-1, 16-11
 (3) MST3.G.G.67 Students find the length of a line segment, given its endpoints.
Students find the length of a line segment, given its endpoints. 1-6 Amsco A: 10-1, 10-2
 (2) MST3.G.G.54 Students define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation.
Students define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation. 1-7 Amsco A: 11-5, 11-6, 11-7
 (2) MST3.G.G.56 Students identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism.
Students identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism. 1-7 Amsco B: 13-6
 (2) MST3.G.G.55 Students investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections.
Students investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections. 1-7 Holt: Technology Lab

Amsco B: 13-6
Art History - wall of the Alhambra
 (1) MST3.G.G.24 Students determine the negation of a statement and establish its truth value.
Chapter 2
Students determine the negation of a statement and establish its truth value.
2-2 Amsco A: 7-2
 (1) MST3.G.G.25 Students know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true.
Students know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true. 2-2, 2-4 Holt:
Chapter 2 Extension
Amsco A: 7-2, 7-3
 (1) MST3.G.G.26 Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences.
Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences. 2-4 Holt:
Amsco A: 7-6, 7-7
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Students write a proof arguing from a given hypothesis to a given conclusion. 2-6 Holt:
Geometry Lab 2-6
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Chapter 3
Students write a proof arguing from a given hypothesis to a given conclusion
3-2, 3-3, 3-4 Amsco B: 3-13 Music History - construction of piano strings
 (2) MST3.G.G.18 Students construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction.
Students construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction. 3-3, 3-4 Holt:  Geometry Labs 3-4
Pg. 181
Amsco A: 24-1
Earth Science - rip currents

Music History - fret and string construction on a guitar
 (1) MST3.G.G.35 Students determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines.
Students determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines. 3-3 Amsco A: 10-4 Carpentry - plumb line
 (3) MST3.G.G.19 Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction.
Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction. 3-3 Holt: Geometry Lab
Amsco A: 24-2
 (1) MST3.G.G.62 Students find the slope of a perpendicular line, given the equation of a line.
Students find the slope of a perpendicular line, given the equation of a line. 3-6 Amsco A: 16-4, 16-5
 (1) MST3.G.G.63 Students determine whether two lines are parallel, perpendicular, or neither, given their equations.
Students determine whether two lines are parallel, perpendicular, or neither, given their equations. 3-6 Amsco A: 16-5
 (1) MST3.G.G.64 Students find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line.
Students find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line. 3-6 Amsco A: 16-5
 (1) MST3.G.G.65 Students find the equation of a line, given a point on the line and the equation of a line parallel to the desired line.
Students find the equation of a line, given a point on the line and the equation of a line parallel to the desired line. 3-6 Amsco A: 16-5
 (1) MST3.G.G.70 Students solve systems of equations involving one linear equation and one quadratic equation graphically.
Students solve systems of equations involving one linear equation and one quadratic equation graphically. Holt: Skills Bank
Pg. S69
 (1) MST3.G.G.30 Students investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle.
Chapter 4
Students investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle.
4-2 Holt: Geometry Lab
Pg. 222
Amsco A: 10-5
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Students write a proof arguing from a given hypothesis to a given conclusion. 4-2, 4-4, 4-5, 4-6, 4-7 Amsco B: 13-3
 (1) MST3.G.G.32 Students investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem.
Students investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem. 4-2 Amsco A: 10-5
Holt:
Pg. 231-237
 (1) MST3.G.G.28 Students determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles.
Students determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles. 4-4, 4-5, 4-6 Holt:
Geometry Lab 4-4
Pg. 240-241

Holt:
Technology Lab
4-5
Pg. 250-251

Amsco A: 11-2, 11-3
 (1) MST3.G.G.29 Students identify corresponding parts of congruent triangles.
Students identify corresponding parts of congruent triangles. 4-3, 4-6 Amsco A: 11-2
 (3) MST3.G.G.67 Students find the length of a line segment, given its endpoints.
Students find the length of a line segment, given its endpoints. 4-6, 4-7 Amsco A: 9-7
 (5) MST3.G.G.69 Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas. 4-6

4-7
Amsco A: 16-10, 16-11
 (3) MST3.G.G.66 Students find the midpoint of a line segment, given its endpoints.
Students find the midpoint of a line segment, given its endpoints. 4-7 Amsco A: 16-11
 (1) MST3.G.G.31 Students investigate, justify, and apply the isosceles triangle theorem and its converse.
Students investigate, justify, and apply the isosceles triangle theorem and its converse. 4-8 Holt:
Pg. 273-279 & 281

Amsco A: 10-6
 (2) MST3.G.G.17 Students construct a bisector of a given angle, using a straightedge and compass, and justify the construction. (2) MST3.G.G.18 Students construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction. (3) MST3.G.G.19 Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction.
Students construct a bisector of a given angle, using a straightedge and compass, and justify the construction.

Students construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction.

Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction.
Holt:
Chapter 4 Extension
Pg. 282-283

Amsco A: 24-1, 24-2
Chapter 4 Extension
Pg. 282-283
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Chapter 5
Students write a proof arguing from a given hypothesis to a given conclusion.
5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7, 5-8
 (1) MST3.G.G.68 Students find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment.
Students find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment. 5-1, 5-2 Amsco A: p.842
 (1) MST3.G.G.21 Students investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles.
Students investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles. 5-2, 5-3 Holt:
Technology Lab
5-3
 (1) MST3.G.G.43 Students investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1.
Students investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1. 5-3
 (3) MST3.G.G.66 Students find the midpoint of a line segment, given its endpoints.
Students find the midpoint of a line segment, given its endpoints. 5-3 Amsco A: 16-11
 (1) MST3.G.G.42 Students investigate, justify, and apply theorems about geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle.
Students investigate, justify, and apply theorems about geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle. 5-4
 (2) MST3.G.G.46 Students investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle.
Students investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle. 5-4 Amsco A: 12-13
 (5) MST3.G.G.69 Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas. 5-4 Holt:
 (1) MST3.G.G.33 Students investigate, justify, and apply the triangle inequality theorem.
Students investigate, justify, and apply the triangle inequality theorem. 5-5 Amsco B: 5-4
Holt:
Geometry Lab 5-5
 (1) MST3.G.G.34 Students determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle.
Students determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle. 5-5
 (2) MST3.G.G.48 Students investigate, justify, and apply the Pythagorean theorem and its converse.
Students investigate, justify, and apply the Pythagorean theorem and its converse. 5-7, 5-8 Holt:
Geometry Lab 5-7
Amsco: 21-4
 (3) MST3.G.G.19 Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction.
Students construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction. Geometry Lab 5-8 Holt:

Amsco: Pg. 837
 (1) MST3.G.G.36 Students investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons.
Chapter 6
Students investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons.
6-1 Holt:
Geometry Lab 6-1

Amsco B: 6-9
 (1) MST3.G.G.37 Students investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons.
Students investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons. 6-1 Holt:
Geometry Lab 6-1

Amsco B: 6-9
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Students write a proof arguing from a given hypothesis to a given conclusion. 6-2, 6-3, 6-4, 6-5, 6-6
 (1) MST3.G.G.38 Students investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals.
Students investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals. 6-2, 6-3 Holt:
Geometry Lab 6-2
 (5) MST3.G.G.69 Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas. 6-2, 6-3, 6-4, 6-5 Holt:
 (1) MST3.G.G.39 Students investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals.
Students investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals. 6-4, 6-5 Technology Lab
6-5

Amsco B: 7-2
 (1) MST3.G.G.41 Students justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids.
Students justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids. 6-5 Amsco A: 11-3
 (1) MST3.G.G.40 Students investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals.
Students investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals. 6-6 Technology Lab
6-6

Amsco B: 7-7
 (1) MST3.G.G.44 Students establish similarity of triangles, using the following theorems: AA, SAS, and SSS.
Chapter 7
Students establish similarity of triangles, using the following theorems: AA, SAS, and SSS.
7-3 Technology Lab
7-3
 (2) MST3.G.G.45 Students investigate, justify, and apply theorems about similar triangles.
Students investigate, justify, and apply theorems about similar triangles. 7-3, 7-4, 7-5, 7-6 Technology Lab
7-4
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Students write a proof arguing from a given hypothesis to a given conclusion. 7-3, 7-4, 7-5, 7-6 Amsco A: 12-10
 (2) MST3.G.G.46 Students investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle.
Students investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle. 7-4
 (2) MST3.G.G.59 Students investigate, justify, and apply the properties that remain invariant under similarities.
Students investigate, justify, and apply the properties that remain invariant under similarities. 7-6
 (5) MST3.G.G.69 Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas. 7-6 Read to Go On?
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Chapter 8
Students write a proof arguing from a given hypothesis to a given conclusion
8-1, 8-5 Ready to Go On?
8-5
 (2) MST3.G.G.45 Students investigate, justify, and apply theorems about similar triangles.
Students investigate, justify, and apply theorems about similar triangles 8-1 Amsco A: 12-10
Amsco B: 8-8
 (1) MST3.G.G.47 Students investigate, justify, and apply theorems about mean proportionality: the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg

Students investigate, justify, and apply theorems about mean proportionality:

• the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse
• the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg

8-1 Amsco A: 12-10
Amsco B: 8-8
 (3) MST3.G.G.67 Students find the length of a line segment, given its endpoints.
Students find the length of a line segment, given its endpoints 8-3 Holt:
Amsco A: 16-10
Amsco B: 1-6
 (5) MST3.G.G.69 Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
Chapter 9
Students investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas.
9-4, 9-5 Holt:
9-5
Amsco B: 7-8
 (2) MST3.G.G.10 Students know and apply that the lateral edges of a prism are congruent and parallel.
Chapter 10
Students know and apply that the lateral edges of a prism are congruent and parallel.
10-1
 (2) MST3.G.G.14 Students apply the properties of a cylinder, including: bases are congruent volume equals the product of the area of the base and the altitude lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base

Students apply the properties of a cylinder, including:

• bases are congruent
• volume equals the product of the area of the base and the altitude
• lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base

• 10-1, 10-4 Amsco A: 4-9
 (1) MST3.G.G.1 Students know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them.
Students know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them. Appendix A-1
 (1) MST3.G.G.2 Students know and apply that through a given point there passes one and only one plane perpendicular to a given line.
Students know and apply that through a given point there passes one and only one plane perpendicular to a given line. Appendix A-1
 (1) MST3.G.G.3 Students know and apply that through a given point there passes one and only one line perpendicular to a given plane.
Students know and apply that through a given point there passes one and only one line perpendicular to a given plane. Appendix A-1
 (1) MST3.G.G.4 Students know and apply that two lines perpendicular to the same plane are coplanar.
Students know and apply that two lines perpendicular to the same plane are coplanar. Appendix A-1
 (1) MST3.G.G.6 Students know and apply that if a line is perpendicular to a plane, then any line perpendicular to the given line at its point of intersection with the given plane is in the given plane.
Students know and apply that if a line is perpendicular to a plane, then any line perpendicular to the given line at its point of intersection with the given plane is in the given plane. Appendix A-1
 (1) MST3.G.G.5 Students know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane.
Students know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane. Appendix A-2
 (1) MST3.G.G.7 Students know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane.
Students know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane. Appendix A-2
 (1) MST3.G.G.8 Students know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines.
Students know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines Appendix A-3
 (1) MST3.G.G.9 Students know and apply that if two planes are perpendicular to the same line, they are parallel.
Students know and apply that if two planes are perpendicular to the same line, they are parallel. Appendix A-3
 (2) MST3.G.G.10 Students know and apply that the lateral edges of a prism are congruent and parallel.
Students know and apply that the lateral edges of a prism are congruent and parallel. Appendix A-3 Amsco A: 4-9
 (1) MST3.G.G.13 Students apply the properties of a regular pyramid, including: lateral edges are congruent lateral faces are congruent isosceles triangles volume of a pyramid equals one-third the product of the area of the base and the altitude

Students apply the properties of a regular pyramid, including:

• lateral edges are congruent
• lateral faces are congruent isosceles triangles
• volume of a pyramid equals one-third the product of the area of the base and the altitude
• 10-5, 10-7 Amsco A: 4-9
 (1) MST3.G.G.15 Students apply the properties of a right circular cone, including: lateral area equals one-half the product of the slant height and the circumference of its base volume is one-third the product of the area of its base and its altitude

Students apply the properties of a right circular cone, including:

• lateral area equals one-half the product of the slant height and the circumference of its base
• volume is one-third the product of the area of its base and its altitude
• 10-5, 10-7 Amsco A: 4-9
 (1) MST3.G.G.11 Students know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal.
Students know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal. 10-6 Amsco A: 4-9
 (2) MST3.G.G.14 Students apply the properties of a cylinder, including: bases are congruent volume equals the product of the area of the base and the altitude lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base

Students apply the properties of a cylinder, including:

• bases are congruent
• volume equals the product of the area of the base and the altitude
• lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base
• 10-6
Technology Lab
10-8
Amsco A: 4-9
 (1) MST3.G.G.12 Students know and apply that the volume of a prism is the product of the area of the base and the altitude.
Students know and apply that the volume of a prism is the product of the area of the base and the altitude 10-6
Technology Lab
10-8
Amsco A: 4-9
 (1) MST3.G.G.16 Students apply the properties of a sphere, including: the intersection of a plane and a sphere is a circle a great circle is the largest circle that can be drawn on a sphere two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles surface area is 4πr2 volume is 4/3πr3

Students apply the properties of a sphere, including:

• the intersection of a plane and a sphere is a circle
• a great circle is the largest circle that can be drawn on a sphere
• two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles
• formula for surface area:  SA = 4 pi r2
• formula for volume:  V = 4/3 pi r3
• Extension
Chapter 10
Amsco A: 4-9
 (8) MST3.G.G.27 Students write a proof arguing from a given hypothesis to a given conclusion.
Chapter 11
Students write a proof arguing from a given hypothesis to a given conclusion.
11-1, 11-2, 11-4, 11-5, 11-6 Holt:
11-2
 (1) MST3.G.G.50 Students investigate, justify, and apply theorems about tangent lines to a circle: a perpendicular to the tangent at the point of tangency two tangents to a circle from the same external point common tangents of two non-intersecting or tangent circles

Students investigate, justify, and apply theorems about tangent lines to a circle:

• a perpendicular to the tangent at the point of tangency
• two tangents to a circle from the same external point
• common tangents of two non-intersecting or tangent circles
• 11-1,
Appendix A-7
Amsco B: 11-2, 11-4
 (1) MST3.G.G.52 Students investigate, justify, and apply theorems about arcs of a circle cut by two parallel lines.
Students investigate, justify, and apply theorems about arcs of a circle cut by two parallel lines. Appendix A-7
 (1) MST3.G.G.49 Students investigate, justify, and apply theorems regarding chords of a circle:: perpendicular bisectors of chords the relative lengths of chords as compared to their distance from the center of the circle

Students investigate, justify, and apply theorems regarding chords of a circle:

• perpendicular bisectors of chords
• the relative lengths of chords as compared to their distance from the center of the circle
• 11-2 Amsco B: 11-2
 (1) MST3.G.G.51 Students investigate, justify, and apply theorems about the arcs determined by the rays of angles formed by two lines intersecting a circle when the vertex is: inside the circle (two chords) on the circle (tangent and chord) outside the circle (two tangents, two secants, or tangent and secant)

Students investigate, justify, and apply theorems about the arcs determined by the rays of angles formed by two lines intersecting a circle when the vertex is:

• inside the circle (two chords)
• on the circle (tangent and chord)
• outside the circle (two tangents, two secants, or tangent and secant)
• 11-4, Technology Lab (11-5), 11-5 Amsco B: 11-4, 11-5
 (1) MST3.G.G.53 Students investigate, justify, and apply theorems regarding segments intersected by a circle: along two tangents from the same external point along two secants from the same external point along a tangent and a secant from the same external point along two intersecting chords of a given circle

Students investigate, justify, and apply theorems regarding segments intersected by a circle:

• along two tangents from the same external point
• along two secants from the same external point
• along a tangent and a secant from the same external point
• along two intersecting chords of a given circle
• Technology Lab
(11-6), 11-6
Amsco B: 11-6
 (1) MST3.G.G.71 Students write the equation of a circle, given its center and radius or given the endpoints of a diameter.
Students write the equation of a circle, given its center and radius or given the endpoints of a diameter. 11-7
 (1) MST3.G.G.72 Students write the equation of a circle, given its graph. Note: The center is an ordered pair of integers and the radius is an integer.
Students write the equation of a circle, given its graph. Note: The center is an ordered pair of integers and the radius is an integer. 11-7
 (1) MST3.G.G.73 Students find the center and radius of a circle, given the equation of the circle in center-radius form.
Students find the center and radius of a circle, given the equation of the circle in center-radius form. 11-7
 (1) MST3.G.G.74 Students graph circles of the form (x - h)2+ (j - k)2 = r2.
Students graph circles of the form (x - h)2+ (j - k)2 = r2. 11-7 Holt:
 (1) MST3.G.G.22 Students solve problems using compound loci.
Students solve problems using compound loci. Chapter 11 Extension Amsco A: 23-7
 (1) MST3.G.G.23 Students graph and solve compound loci in the coordinate plane.
Students graph and solve compound loci in the coordinate plane. Chapter 11 Extension Amsco A: 23-7
 (2) MST3.G.G.55 Students investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections.
Chapter 12
Students investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections.
Appendix A-4
(Chapter 12)
 (2) MST3.G.G.59 Students investigate, justify, and apply the properties that remain invariant under similarities.
Students investigate, justify, and apply the properties that remain invariant under similarities. Appendix A-4
(Chapter 12)
 (2) MST3.G.G.54 Students define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation.
Students define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections) Note: Use proper function notation. 12-1, 12-2, 12-3,
Technology Lab
12-4, 12-6
Holt:
12-4
 (2) MST3.G.G.56 Students identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism.
Students identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism. 12-1, 12-2, 12-3 Amsco B: 13-1
 (1) MST3.G.G.61 Students investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90° and 180°, reflections over the lines x = 0, and y = x, and dilations centered at the origin.
Students investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90° and 180°, reflections over the lines x = 0, and y = x, and dilations centered at the origin. 12-1, 12-2, 12-3
Appendix A-6
(Chapter 12), 12-4, 12-7
Holt:
12-4
Amsco B: 13-2
 (1) MST3.G.G.57 Students justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections).
Students justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections). Appendix A-5
(Chapter 12)
 (1) MST3.G.G.58 Students define, investigate, justify, and apply similarities (dilations and the composition of dilations and isometries).
Students define, investigate, justify, and apply similarities (dilations and the composition of dilations and isometries). 12-7, Chapter 12 Extension Holt: