1. Unit 2 Similarity, Congruence, and Proofs
GSE Geometry
Unit 2 Similarity, Congruence, and Proofs

2. Triangle Theorems
Triangle Sum Theorem: The 3 a angles in a triangle add up to ______. Exterior Angle Theorem: The 2 remote interior angles add up and equal the exterior angle
180

3. 4 Basic Constructions

7. Example
Correct answer: C

8. Ways to Prove Triangles Congruent

9. Example

10. Solution Mark the given information:
In order to use the SAS postulate, the pair of sides which makes D and J the INCLUDED angles must be congruent, DF and HJ. However, HF is congruent to itself by the reflexive property, so you must have ( )

11. Similar Polygons
Corresponding angles are congruent and Corresponding sides are proportional. Order matters in a similarity statement

12. Solve for x and y. x = 26 cm y = 12 cm L A 5 cm x S 10 cm y 13 cm C BT
x = 26 cm
y = 12 cm

13. In similar triangles, angles are congruent and sides are proportional
Find the missing angle measures. A L 53 S C B 37 T

14. Find the perimeter of the smaller triangle.
12 cm
4 cm
Perimeter = x
Perimeter = 60 cm
x = 20 cm

15. 3 ways to Prove Triangles Similar

16. Determine whether the triangles are similar
Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement.
Yes, AA~
68°
43°
68°
43° V NO Y 7 3 5 Z X W 11 U

17. SAS~ 12 4 5 15 Prove that RST ~ PSQ 1. Two sides are proportional
2. Included angle is congruent
SAS~ R S T P Q 12 4 5 15