Geometry Next Gen
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15 days including 2 quizzes, test review, and test |
Unit 1 Constructions |
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How can we construct an equilateral triangle and an inscribed equilateral triangle? How can we construct an inscribed hexagon and square? How can we construct an angle bisector and copy an angle? How can we construct a perpendicular bisector and a perpendicular line through a point? How can we construct a parallel line Construct points of Concurrency – circumcenter and incenter?(including the circumscribed circle and inscribed circle of a triangle) What congruencies are formed by each of the above constructions? How can we construct an isosceles triangle(honors)? How can we construct parallel lines by copying angles?(honors) How can we construct a circle?(honors) How can we construct an angle bisector of a rectangle and conclude if it also bisects the opposite angle?(honors)
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Draw Construct Point Segment Ray Equilateral Triangle Intersection Radius Scalene Triangle Isosceles Triangle Inscribed Circumscribed Hexagon Angle Angle Bisector Perpendicular Lines Segment Bisector Parallel Median Altitude Concurrency Circumcenter Incenter Centroid Orthocenter
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I can construct the basic constructions. I can use basic constructions to construct a 30 degree angle, 45 degree angle, divide a segment into 4 equal parts, scalene triangle and isosceles triangle. I can construct the inscribed /circumscribed circles of a triangle. I can state congruencies formed by all constructions.
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Unit 1 Honors Constructions Packet.pdf |
2 Quizzes Test Review Unit Test
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16 days |
Unit 2 Angle Relationships |
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How can we solve for unknown angle measures in various situations? How can we solve for unknown angle measures using auxiliary lines? How can we construct a formal Proof using reasoning, theorems, definitions, etc. involving unknown angle measures? |
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Angles on a line/Linear Pair Angles at a point Vertical angles Complementary angles Supplementary angles Adjacent angles Alternate interior and exterior angles Corresponding angles Same side interior angles Auxiliary lines Triangle sum theorem Isosceles triangle Equilateral triangle Exterior angle theorem Proof Theorem Deductive reasoning Substitution Property Reflexive Property Transitive Property Addition Property Subtraction Property Division Property Distributive Property Symmetric Property |
1. I can solve for angles at a point. 2. I can solve for missing angles on a line 3. I can solve for angles formed by two parallel lines cut by a transversal. 4. I can solve for the exterior angle of a given triangle. 5. I can solve for the missing angle in a triangle. 6. I can solve for the missing angle/s in an isosceles triangle. 7. By using known angle theorems, I can solve/prove for missing measurements in complex diagrams. (using auxilliary lines) **8. Unit 2 project Help find all the missing angles using various Angle Theorems to help design a computer game. (honors)
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Honors Unit 2 Solving for Unkown Angles - Google Docs.pdf |
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16 days including quizzes and tests |
Unit 3 Transformations - rigid motions |
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How can we construct the Line of Reflection and Construct Images Reflected Over a Line? How can we onstruct the Center of Rotation and Rotate a figure 90 degrees? How can we construct a Translation given a vector? How can we perform Reflections, Rotations, and Translations on the coordinate plane using a mapping? How can we identify the number of lines of symmetry, order and angle of rotational symmetry? How can we graph a Composition of Transformation on the coordinate plane? ow can we identify Corresponding Parts of Congruent Figures? How can we use Properties of Rigid Motions to Explain Congruence? How can we identify the symmetries (rotations and reflections) that map a polygon onto itself. |
1. Construct the Line of Reflection and Construct Images Reflected Over a Line 2. Construct the Center of Rotation and Rotate a figure 90 degrees 3. Construct a Translation given a vector 4. Perform Reflections, Rotations, and Translations on the coordinate plane using a mapping. 5. Identify the number of lines of symmetry, order and angle of rotational symmetry 6. Graph a Composition of Transformation on the coordinate plane 7. Identify Corresponding Parts of Congruent Figures 8. Use Properties of Rigid Motions to Explain Congruence 9. Given a polygon, describe the rotations and reflections(symmetries) that carry the polygon onto itself. |
Angle of Rotation Reflection Composition Reflection Symmetry Congruence Regular Polygon Correspondence Point reflection Rigid Motion Rotation Image Rotational Symmetry Line Symmetry Symmetry Mapping Transformation Point Symmetry Translation Polygon Vector Pre-Image |
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Honors U3 Honors REVISED Transformations Student Packet 22 -23 (AutoRecovered).docx |
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25 Days |
Unit 4 Congruent Triangles |
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1. Write congruence statements using given information 2. Prove triangle congruent using SSS, SAS, ASA, AAS and HL 3. Use the Addition, Subtraction, Division Postulates, along with substitution in a formal proof 4. Identify rigid Motions that would map one congruent triangle onto another 5. Prove triangles are congruent and then prove a pair of corresponding parts (angles or sides) congruent by CPCTC 6. Prove Isosceles Triangles, Parallel and Perpendicular lines, medians, and angle bisectors |
Right Angle Postulate Angle Bisector Theorem Segment Bisector Substitution Property Perpendicular Lines Reflexive Property Midpoint Addition Postulate Median Subtraction Postulate Perpendicular Bisector Division Postulate Vertical Angles CPCTC Altitudes Linear Pair Congruence Isosceles triangle Parallel lines |
I can write congruence statements using given information. I can prove triangle congruent using SSS, SAS, ASA, AAS and HL I can use the Addition, Subtraction, Division Postulates, along with substitution in a formal proof. I can identify rigid Motions that would map one congruent triangle onto another. I can prove triangles are congruent and then prove a pair of corresponding parts (angles or sides) congruent by CPCTC I can prove Isosceles Triangles, Parallel and Perpendicular lines, medians, and angle bisectors |
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Unit 5 Quadrilaterals days |
Unit 5 Quadrilaterals |
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How can we apply the properties of quadrilaterals (parallelogram, rectangle, rhombus, square and trapezoid) to find segment lengths and angle measures?
How can we solve algebraic problems related to quadrilaterals using the properties?
How can we prove a quadrilateral is a specific quadrilateral? |
1. Know and apply the properties of quadrilaterals (parallelogram, rectangle, rhombus, square and trapezoid) Kites(honors) 2. Solve algebraic problems related to quadrilaterals using the properties.
3.Complete quadrilateral proofs. |
Properties of a Parallelogram Properties of a Rectangle Properties of a Rhombus Properties of a Square Properties of an Isosceles Trapezoid Properties of a Trapezoid Quadrilateral Properties of a kite (honors) |
I can apply the properties of quadrilaterals (parallelogram, rectangle, rhombus, square and trapezoid) to find segment lengths and angle measures. Kite(Honors) I can solve algebraic problems related to quadrilaterals using the properties.
I can complete quadrilateral proofs. |
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Unit 6 Similar Triangles |
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How can we construct a dilation(scale drawing)? How can we state and graph a dilation on the coordinate plane? How can we prove triangles similar? How can we prove that sides of similar triangles are in proportion? How can we prove that in a true proportion, the product of the means = the product of the extremes? How can we find missing side lengths and angle measures using the mid-segment theorem? How can we use the side splitter theorem to find missing lengths in similar triangles? How can we find missing lengths given 3 or more parallel lines cut by 2 transversals? How can we compare the ratio of the sides, perimeters, areas and volumes of similar triangles? How can we use the Angle Bisector Theorem to find missing lengths? |
1. Construct a dilation(scale drawing) 2. State and graph a dilation on the coordinate plane 3. Prove triangles similar 4. Prove that sides of similar triangles are in proportion 5. Prove that in a true proportion, the product of the means = the product of the extremes 6. Find missing side lengths and angle measures using the mid-segment theorem 7. Use the side splitter theorem to find missing lengths in similar triangles 8. Find missing lengths given 3 or more parallel lines cut by 2 transversals. 9. Compare the ratio of the sides, perimeters, areas and volumes of similar triangles 10. Use the Angle Bisector Theorem to find missing lengths |
Dilation Proportion Scale Factor Angle Bisector Center of Dilation Ratio of the sides Mid-Segment Ratio of the area Side-Splitter Theorem Ratio of the volumes |
I can write congruence statements using given information. I can prove triangle congruent using SSS, SAS, ASA, AAS and HL. I can use the Addition, Subtraction, Division Postulates, along with substitution in a formal proof. I can identify rigid Motions that would map one congruent triangle onto another. I can prove triangles are congruent and then prove a pair of corresponding parts (angles or sides) congruent by CPCTC. I can prove Isosceles Triangles, Parallel and Perpendicular lines, medians, and angle bisectors. |
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Unit 7 Right Triangle Trig |
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How can we solve algebraic equations that contain radicals using all mathematical operations? How can we solve for missing side lengths when an altitude is drawn to the hypotenuse of a right triangle? How can we solve for side lengths in right triangles using the Pythagorean Theorem? How can we solve for side lengths in Special Right Triangles using ratios? How can we solve for side or angle measures in right triangles using Trigonometry Functions (sine, cosine, tangent)? How can we use the sine and cosine complement rule to find missing angles? How can we use the Trigonometric Identities to find missing side and angle measures? |
1. Solve algebraic equations that contain radicals using all mathematical operations. 2. Solve for missing side lengths when an altitude is drawn to the hypotenuse of a right triangle. 3. Solve for side lengths in right triangles using the Pythagorean Theorem. 4. Solve for side lengths in Special Right Triangles using ratios. 5. Solve for side or angle measures in right triangles using Trigonometry Functions (sine, cosine, tangent). 6. Understand and use sine and cosine complements. 7. Understand and use the Trigonometric Identities.
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Rationalize the Denominators Sine Cosine Tangent Reference Angle Opposite Side Adjacent Side Hypotenuse Angle of Elevation Angle of Depression |
I can solve algebraic equations that contain radicals using all mathematical operations. I can solve for missing side lengths when an altitude is drawn to the hypotenuse of a right triangle. I can solve for side lengths in right triangles using the Pythagorean Theorem. I can solve for side lengths in Special Right Triangles using ratios. I can solve for side or angle measures in right triangles using Trigonometry Functions (sine, cosine, tangent). I can use sine and cosine complements. I can understand and use the Trigonometric Identities. |
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Unit 8 Perimeter, Area, Volume |
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How can we use the area formulas to solve for areas in regular figures, compound figures and answer shaded region questions? How can we answer questions about relationships of figures in three dimensional space? How can we find the volumes of prisms and answer questions about their cross sections? How can we find the density of a figure or use a figures density to determine mass or volume for a figure? How can we apply Cavalier’s Principle to find the volume or base area for a figure? How can we use the Scaling Principle for Volume? |
1. Use the area formulas to solve for areas in regular figures, compound figures and answer shaded region questions. 2. Answer questions about relationships of figures in three dimensional space. 3. Find the volumes of prisms and answer questions about their cross sections. 4. Find the density of a figure or use a figures density to determine mass or volume for a figure. 5. Apply Cavalier’s Principle to find the volume or base area for a figure. 6. Use the Scaling Principle for Volume. |
Volume Area Perimeter Cylinder Prism Pyramid Cone Sphere Cross-section Cavalieri's Principle Oblique Right Base Edge Vertex Lateral face Density Mass |
I can use the area formulas to solve for areas in regular figures, compound figures and answer shaded region questions. I can answer questions about relationships of figures in three dimensional space. I can find the volumes of prisms and answer questions about their cross sections. I can find the density of a figure or use a figures density to determine mass or volume for a figure. I can apply Cavalier’s Principle to find the volume or base area for a figure. I can use the Scaling Principle for Volume.
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