





(1) 
GC.1 
Prove that all circles are similar 

(2) 
GSRT.5 
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 

Lesson 2

101 Circles and Circumference

Circle
Diameter
Radius

1g

(1) 
GC.2 
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle. 

(2) 
GCO.10 
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians of a triangle
meet at a point. 
(2) 
GCO.11 
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals. 
(2) 
GCO.9 
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and orresponding angles are congruent;
points on a perpendicular bisector of a line segment are exactly those
equidistant from the segment's endpoints. 

Lessons 16, 1116

102 Measuring Angles and Arcs
103 Arcs and Chords
104 Inscribed Angles

Inscribed Angle
Central Angle
Radius
Chord
Diameter
Tangent Line

1a, 2abc

(1) 
GC.3 
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 

(1) 
GCO.12 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the
line. 
(1) 
GCO.3 
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 
(1) 
GCO.5 
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will
carry a given figure onto another. 

Lessons 16

104 Inscribed Angles
105 Tangents

Inscribed Angle
Cyclic Quadrilateral

3abc

(1) 
GC.5 
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the
formula for the area of a sector. 

(2) 
GSRT.5 
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 

Lessons 710

102 Measuring Angles and Arcs
113 Areas of Circles and Sectors

Arc Length
Radius
Sector

1bcde







(1) 
GGPE.1 
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 

(1) 
8.G.7 
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and
three dimensions. 


108 Equations of Circles

Radius

4ab

(1) 
GGPE.4 
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies
on the circle centered at the origin and containing the point (0, 2). 

(1) 
8.G.8 
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 
(2) 
GCO.10 
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians of a triangle
meet at a point. 
(2) 
GCO.11 
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals. 
(2) 
GCO.9 
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and orresponding angles are congruent;
points on a perpendicular bisector of a line segment are exactly those
equidistant from the segment's endpoints. 

Lessons 1721

48 Triangles and Coordinate Proof
62 Parallelograms
63 Tests for Parallelograms
64 Rectangles
65 Rhombi and Squares
66 Trapezoids and Kites


1f, 5

(1) 
GMG.1 
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 



11 Points, Lines, and Planes
17 Threedimensional Figures
61 Angles of Polygons
115 Areas of Similar Figures
123 Surface Areas of Pyramids and Cones (include Prisms)


