Geometry

Prove that all circles are similar

Identify and describe relationships among inscribed angles, radii, and chords
Lesson SetsGC.2
1. Relate central angles, arc measure, and arc lengthGC.2

2. Find measures of inscribed angles using central anglesGC.2

3. Understand that tangents are perpendicular to radiiGC.2

4. Find relationships between central and circumscribed anglesGC.2

5. Find missing angle measurements within a circle using the intersect...GC.2


Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

Give arguments for formulas of circucircumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems

Identify the shapes of twodimensional crosssections of threedimensional objects and the threedimensional objects generated by rotations of twodimensional objects

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar
Lesson SetsGSRT.3
1. Show triangle similarity using translationGSRT.3

2. Establish triangle similarity using translation and dilationGSRT.3

3. Determine triangle similarity by checking for corresponding congrue...GSRT.3

4. Prove AA similarity by overlapping anglesGSRT.3

5. Understand why the third angles of similar triangles are congruentGSRT.3


Prove theorems about triangles
Lesson SetsGSRT.4
1. Understand that a line parallel to one side of a triangle intersect...GSRT.4

2. Understand that a line dividing two sides of a triangle proportiona...GSRT.4

3. Prove that two triangles are similar by writing an algebraic proofGSRT.4

4. Prove triangle similarity algebraicallyGSRT.4

5. Use similarity to prove the Pythagorean TheoremGSRT.4


Solve problems and to prove relationships in geometric figures
Lesson SetsGSRT.5 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle
Lesson Sets 
Explain and use the relationship between the sine and cosine of complementary angles
Lesson SetsGSRT.7
1. Understand that acute angles of right triangles are complementaryGSRT.7

2. Graph circles using the Pythagorean TheoremGSRT.7

3. Find coordinates for the 30ᴼ and 60ᴼ angles of the unit circleGSRT.7

4. Find coordinates for the 45ᴼ angle of the unit circleGSRT.7

5. Find all trigonometric coordinates on the unit circleGSRT.7

6. Relate sine and cosine values using the unit circleGSRT.7


Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems
Lesson SetsGSRT.8
1. Find right triangle angle measures using inverse sine functionGSRT.8

2. Find right triangle angle measures using inverse cosine functionGSRT.8

3. Find right triangle angle measures using inverse tangent functionGSRT.8

4. Solve nonright triangles using Law of SinesGSRT.8

5. Solve nonright triangles using Law of CosinesGSRT.8

6. Apply trigonometry and the Pythagorean Theorem in contextGSRT.8
