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

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

4 Basic Constructions

Example Correct answer: C

Ways to Prove Triangles Congruent

Example

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 ( )

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

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

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

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

3 ways to Prove Triangles Similar

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

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