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# Chapter 4 - PowerPoint PPT Presentation

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.

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### Chapter 4

4.2 Congruence & Triangles

• Identify congruent figures and corresponding parts

• Prove that two triangles are congruent

• Assignment: 1-29 all, quiz page 210

• 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

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

• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also 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

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

• 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

• 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

P

G

24°

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