1. 4.2 Congruence & Triangles
Chapter 4
4.2 Congruence & Triangles

2. Goal 1: Identifying Congruent Figures
Two geometric figures are congruent if they have exactly the same size and shape.
When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

3. ABC =̃ PQR A & P B & Q C & R AB & PQ BC & QR CA & RP B Q C P R A
What are the corresponding angles?
What are the corresponding sides?
A & P
B & Q
C & R
AB & PQ
BC & QR
CA & RP

4. Theorem 4.3: Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

5. Theorem 4.4: Properties of Congruent Triangles
Reflexive Property of Congruent Triangles: Every triangle is congruent to itself
Symmetric Property of Congruent Triangles: If ABC =̃ DEF, then DEF =̃ ABC
Transitive Property of Congruent Triangles:
If ABC =̃ DEF and DEF =̃ JKL, than
ABC =̃ JKL

6. Goal 2: Proving Triangles are Congruent
Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o. Prove: ΔRQP  ΔMQN R N
92o Q
92o M P

7. Statements Reasons 1.seg RP  seg MN 1. given seg PQ  seg NQ
Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o. Prove: ΔRQP  ΔMQN
Statements Reasons
1.seg RP  seg MN given
seg PQ  seg NQ
seg RQ  seg MQ
mP=92o & mN is 92o
2. mP=mN trans. prop =
3. P  N def of  s
4. RQP  MQN vert s thm
5. R  M rd s thm
6. ΔRQP  Δ MQN def of  Δs

8. Practice Problems Name the congruent figures
Given M =̃ G and P =̃ H, find the value of x. E B D A C F
(2X-50)° H M
142° N J
24° P G

9. More Practice Problems
Given that N =̃ R and L =̃ S, find the value of x.
Given that LMN =̃ PQR, answer the following:
mP= QR =̃
mM= LN =̃
mR=
mN= R M S
(2X+30)° N
55°
65° L T P N Q
45° R L
105° M