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4.3 Congruent Triangles

- We will
- name and label corresponding parts of

congruent triangles. - identify congruence transformations.

Corresponding parts of congruent triangles

- Triangles that are the same size and shape are

congruent triangles. - Each triangle has three angles and three sides.

If all six corresponding parts are congruent,

then the triangles are congruent.

Corresponding parts of congruent triangles

If ?ABC is congruent to ?XYZ , then vertices of

the two triangles correspond in the same order as

the letter naming the triangles.

Corresponding parts of congruent triangles

This correspondence of vertices can be used to

name the corresponding congruent sides and angles

of the two triangles.

- Definition of Congruent Triangles (CPCTC)
- Two triangles are congruent if and only if their

corresponding parts - are congruent.
- CPCTC
- Corresponding Parts of Congruent Triangles are

Congruent

Example 3-1a

ARCHITECTURE A tower roof is composed of

congruent triangles all converging toward a

point at the top. Name the corresponding

congruent angles and sides of ?HIJ and ?LIK.

Example 3-1c

Answer

Properties of Triangle Congruence

- Congruence of triangles is reflexive, symmetric,

and transitive. - REFLEXIVE

?JKL ?JKL

K

K

L

L

J

J

Properties of Triangle Congruence

- Congruence of triangles is reflexive, symmetric,

and transitive. - SYMMETRIC

If ?JKL ?PQR, then ?PQR ?JKL.

K

Q

L

R

J

P

Properties of Triangle Congruence

- Congruence of triangles is reflexive, symmetric,

and transitive. - TRANSITIVE

If ?JKL ?PQR, and ?PQR ?XYZ, then ?JKL

?XYZ.

K

Q

L

R

J

Y

P

Z

X

IDENTIFY CONGRUENCE TRANSFORMATIONS

If you?ABC down and to the right, it is

still congruent to ?DEF.

B

C

A

IDENTIFY CONGRUENCE TRANSFORMATIONS

If you turn ?ABC, it is still congruent to ?DEF.

A

B

C

IDENTIFY CONGRUENCE TRANSFORMATIONS

If you flip ?ABC, it is still congruent to ?DEF.

A

C

B

Example 3-2a

Example 3-2b

Use the Distance Formula to find the length of

each side of the triangles.

Example 3-2b

Use the Distance Formula to find the length of

each side of the triangles.

Example 3-2b

Use the Distance Formula to find the length of

each side of the triangles.

Example 3-2c

TempCopy

Use a protractor to measure the angles of the

triangles. You will find that the measures are

the same.

Example 3-2d

COORDINATE GEOMETRY The vertices of ?RST are

R(-3, 0), S(0, 5), and T(1, 1). The vertices of

?R?S?T ? are R?(3, 0), S?(0, -5), and T?(-1, -1).

Name the congruence transformation for ?RST and

?R?S?T?.

Answer ?R?S?T? is a turn of ?RST.

Example 3-2f

COORDINATE GEOMETRY The vertices of ?ABC are

A(5, 5), B(0, 3), and C(4, 1). The vertices of

?A?B?C? are A?(5, 5), B?(0, 3), and C?(4, 1).

Answer

Use a protractor to verify that corresponding

angles are congruent.

Example 3-2g

b. Name the congruence transformation for ?ABC

and ?A?B?C?.

Answer turn

- BOOKWORK
- p. 195 9 19,
- 22 25 (just name the congruence

transformation) - HOMEWORK
- p.198 Practice Quiz

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