Section 4.5

Warm Up

1. Name all sides and angles of ∆FGH.

2. What is true about K and L? Why?

3. What does it mean for two segments to be congruent?

Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

Each triangle is made up of six parts:3 sides and 3 angles

If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

Corresponding PartsCorresponding Parts

ABC DEF

B

A C

E

D

F

1. AB DE

2. BC EF

3. AC DF

4. A D

5. B E

6. C F

CPCTCCorresponding Parts of Congruent Triangles are Congruent.

Congruency amongst triangles does not change when you…

slide (translation),

Turn (rotation),

or flip (reflection) … the triangles.

EXAMPLE 1 Identify congruent parts

Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

SOLUTION

The diagram indicates that JKL TSR.

Corresponding sides JK TS KL SR LJ RT

Corresponding angles J T, K S, L R

Complete each congruence statement.

Write a congruence statement.

Given ΔBCD = ΔRST, m C = 57, m R = 64, m D = 5x + 4. Find x and m T.

Given ΔQRS = ΔLMN, RS = 8, QR=14, QS=10, MN = 3x – 25. Find x.

Name the corresponding angles and sides if ΔBCD = ΔEFG.

Given ΔCAT = ΔDOG, CA=14, AT=18, TC=21 and DG=2x+7, find the value of x.

Given: ∆ABC ∆DBC. Find the value of x and mDBC.

Given: ∆ABC ∆DEFFind the value of x.

Find mF.

Lesson Quiz

1. ∆ABC ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.

Given that polygon MNOP polygon QRST, identify the congruent corresponding part.

2. NO ____ 3. T ____