Two Proof-Oriented Triangle Theorems Lesson 7.2. Theorem 53:If 2 angles of one triangle are congruent to two angles of a second triangle, then the third.

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Two Proof-Oriented Triangle Theorems Lesson 7.2

Theorem 53:If 2 angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. (no-choice Theorem) If <A congruent <D <B congruent <E Then <C congruent <F Since the sum = 180 subtract and get <C congruent <F The triangles do not have to be congruent, the angles do! A F C B DE

Theorem 54: If there exists a correspondence between the vertices of two triangles such that two angles and a non-included side of one triangle are congruent to the corresponding parts of the other, then the triangles are congruent. (AAS)

Given:JM  GM GK  KJ Conclude: <G  <J G M H J K 1. JM  GM, GK  KJ 2.  GMJ,  JKG rt  s 3.  GMJ   JKG 4.  GHM,  JHK vert  s 5.  GHM   JHK 6.  G   J 1.Given 2.  lines from rt  s 3.Rt  s are  4.Assumed from diagram 5.Vert.  s are  6.No Choice Theorem

3x-5 60 x+51 Given: Triangle as marked. Find the m  1. By Ext  Theorem 3x – 5 = 60 + (x + 5) 3x – 5 = 65 + x 2x = 70 x = 35  1 is supp to (3x – 5) Then  1 + (3x – 5) = 180  1 + 3(35) – 5 = 180  – 5 = 180  = 180  1 = 80