http://www.ck12.org Chapter 4. Triangles and Congruence
Solution:To write the congruence statement, you need to line up the corresponding parts in the triangles:^6 R∼=
(^6) F, (^6) S∼= (^6) E,and (^6) T∼= (^6) D. Therefore, the triangles are 4 RST∼= 4 F ED.
Example 3:If 4 CAT∼= 4 DOG, what else do you know?
Solution: From this congruence statement, we can conclude three pairs of angles and three pairs of sides are
congruent.
(^6) C∼= (^6) D (^6) A∼= (^6) O (^6) T∼= (^6) G
CA∼=DO AT∼=OG CT∼=DG
The Third Angle Theorem
Example 4:Findm^6 Candm^6 J.
Solution:The sum of the angles in each triangle is 180◦. So, for 4 ABC, 35 ◦+ 88 ◦+m^6 C= 180 ◦andm^6 C= 57 ◦.
For 4 HIJ, 35◦+ 88 ◦+m^6 J= 180 ◦andm^6 Jis also 57◦.
Notice that we were given thatm^6 A=m^6 Handm^6 B=m^6 Iand we found out thatm^6 C=m^6 J. This can be
generalized into the Third Angle Theorem.
Third Angle Theorem:If two angles in one triangle are congruent to two angles in another triangle, then the third
pair of angles must also congruent.
In other words, for triangles 4 ABCand 4 DEF,^6 A∼=^6 Dand^6 B∼=^6 E, then^6 C∼=^6 F.
Notice that this theorem does not state that the triangles are congruent. That is because if two sets of angles are
congruent, the sides could be different lengths. See the picture to the left.
Example 5:Determine the measure of the missing angles.