Two Proof-Oriented Triangle Theorems

1. Two Proof-Oriented Triangle Theorems Lesson 7.2

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) F C B A D E 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!

3. 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)

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

5. Given: Triangle as marked. Find the m 1. 60 3x-5 x+5 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 1 + 105 – 5 = 180 1 + 100 = 180 1 = 80