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### 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

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, mP=92o and mN 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, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN

Statements Reasons

1.seg RP seg MN 1. given

seg PQ seg NQ

seg RQ seg MQ

2. mP=mN 2. trans. prop =

3. P N 3. def of s

4. RQP MQN 4. vert s thm

5. R M 5. 3rds 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

P

G

24°

More Practice Problems

Given that N =̃ R and L =̃ S, find the value of x.

Given that LMN =̃ PQR, answer the following:

mP= QR =̃

mM= LN =̃

mR=

mN=

R

M

S

(2X+30)°

N

55°

65°

L

T

P

N

Q

45°

R

L

105°

M

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