4.2 Congruence & Triangles Chapter 4 4.2 Congruence & Triangles

Objectives/Assignment Identify congruent figures and corresponding parts Prove that two triangles are congruent Assignment: 1-29 all, quiz page 210

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.

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

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.

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

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 1. given seg PQ  seg NQ seg RQ  seg MQ 2. mP=mN 2. trans. prop = 3. P  N 3. def of  s 4. RQP  MQN 4. vert s thm 5. R  M 5. 3rd s thm 6. ΔRQP  Δ MQN 6. def of  Δs

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

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

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