6th Grade Math Textbook, Fundamentals

9-9

Congruent Triangles

Objective To identify congruent triangles • To explore angle-side relations in triangles

• To use congruent parts of congruent triangles to find missing angle and side measures

 have exactly the same size and shape. Their

corresponding sides and corresponding angles are congruent.

Congruent triangles

ABCADC Triangle ABCis congruent

to triangle ADC.

Corresponding sides:

ACAC

ADAB

DCBC

Corresponding angles:

ABCADC

CABCAD

ACBACD

A

B

C

D

To show that two triangles are congruent, you do not need

to show that allcorresponding parts are congruent.

Use these three statements to identify congruent triangles.

Side-Side-Side(SSS)

If all 3 pairs of corresponding

sides of both triangles are

congruent, the triangles are

congruent.

TUWZYX

T

W U Z

Y X

Side-Angle-Side(SAS)

If 2 pairs of corresponding

sides and the included angles

of both triangles are

congruent, the triangles are

congruent.

FGHLJK

G

F

H

JK

L

An included angleis the angle

between two sides. An included side

is the side between two angles.

Use the corresponding parts of congruent triangles

to find missing angle measures and side lengths.

Remember:Matching tick marks and

angle marks identify corresponding parts.

RSTZXY

Find the measure ofRS.

RSand ZXare corresponding sides.

RSZX, so RS2.5 cm

S

R

T

Y X

Z

6.5 cm 2.5 cm

6 cm

6.5 cm

6 cm

KLMPQN

Find mPQN.

PQNand KLMare corresponding angles.

PQNKLM,so mPQN40°

40

K

L

M

70

(^70) P
Q
N
 &KDSWHU
Angle-Side-Angle(ASA)
If 2 pairs of corresponding
angles and the included sides
of both triangles are
congruent, the triangles are
congruent.
MNPQRS
N
P
M
R
S
Q