Congruent FiguresCongruent figures are two figures that have the same size and shape.

IF two figures are congruent THEN they have the same size and shape.

IF two figures have the same size and shape THEN they are congruent.

Two figures have the same size and shape IFF they are congruent.

Conditional:

Converse:

Biconditional:

Congruent Triangles - CPCTC

If ABC PQR

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

Two triangles are congruent IFF their corresponding parts (angles and sides) are congruent.

BC

A

QR

PA ↔ P; B ↔ Q; C ↔ R

Vertices of the 2 triangles correspond in the same order as the triangles are named.

Corresponding sides and angles of the two congruent triangles:

A

A P B Q C

B PQ BC Q C P

R

R A R

≡

≡

=

=

│

│

Example:

Congruent Triangles

____

____

____

AB

BC

AC

ZY

YX

B

A

C

X Y

Z

≡ ≡=

=

│ │

∆ABC ______

A ____ Z

B _____

C ______

Y

X

∆ ZYX

∆ABC ∆XYZ

Note:

ZX

ZY

Given the following corresponding angles, write a congruence statement. Is there more than one way to write it? If so, list them.

R

AY

S

UN

S

U

N

R

A

YSUN RAY

Also NUS YAR

Also USN ARY

Proving Triangles Congruent

By SSS, SAS, and HL

Included Angles & Sides

& .A is the included angle for AB AC& .B is the included angle for BA BC

& .C is the included angle for CA CB

A

B C

Included Angle:

Included Side:

& .AB is the included side for A B

& .BC is the included side for B C

& .AC is the included side for A C

** *

In a triangle, the angle formed by two sides is the included angle for the two sides.

The side of a triangle that forms a side of two given angles.

Side-Side-SideSSS If the sides of one triangle are congruent to the sides of a

second triangle, then the triangles are congruent.A

B C

D

E F

Side-Angle-Side

SAS If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.

A

B C

D

E F

Right Triangles

In a right triangle, the sides adjacent to theright angle are called the legs. The side opposite theright angle is called the hypotenuse of the right triangle.

leghypotenuse

leg

Hypotenuse-Leg

HL If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

A

B C

D

E F

Decide whether the triangles are congruent.If they are, write a congruence statement.

1. 2.

3. 4.

5.

6.