Lesson: Pages: Objectives: 4.3 Exploring CONGRUENT Triangles 196 – 197 To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles To STATE the CPCTC.

Lesson:

Pages:

Objectives:

4.3 Exploring CONGRUENT Triangles

196 – 197

To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles

To STATE the CPCTC Theorem

• congruent triangles

• congruence transformations

GEOMETRY 4.3

Congruent Polygons have the:

SAME Size

SAME Shape

GEOMETRY 4.3

Congruent Polygons have the:

SAME Size

SAME Shape

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

GEOMETRY 4.3

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

A B

C

D E

F

GEOMETRY 4.3

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

A B

C DE

F

GEOMETRY 4.3

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

Because CORRESPONDING parts determine Congruence:

You may have to:

Slide Rotate, or Flip

Figures to determine whether they are CONGRUENT

GEOMETRY 4.3GEOMETRY 4.3

Congruent TRIANGLES have

Congruent CORRESPONDING SIDES

Congruent CORRESPONDING Angles

The way you NAME the Triangle establishes theCORRESPONDENCE:

GEOMETRY 4.3

To WRITE the CORRESPONDINGParts of Congruent Triangles,use

GEOMETRY 4.3

SO, if ABC FGH:

Congruent Angles Congruent Sides

GEOMETRY 4.3

Congruent Angles Congruent Sides

Be sure to WRITE the LETTERS of VERTICESin the CORRECT ORDER when you write a Statement.

SO, if ABC FGH:

GEOMETRY 4.3

A THEOREM:

Two Triangles are CONGRUENT

if and only if

Their CORRESPONDING PARTS are CONGRUENT

GEOMETRY 4.3

A THEOREM:

Two Triangles are CONGRUENT

if and only if

Their CORRESPONDING PARTS are CONGRUENT

This is called CPCTC

GEOMETRY 4.3

A THEOREM:

Two Triangles are CONGRUENT

if and only if

Their CORRESPONDING PARTS are CONGRUENT

This is called CPCTC(Corresponding Parts of Congruent Triangles are Congruent.)

GEOMETRY 4.3

Name the CORRESPONDING CONGRUENT Angles & Sides.

TRU TSU

GEOMETRY 4.3

CONGRUENCE of TRIANGLES is:

REFLEXIVE

SYMMETRIC, and

TRANSITIVE

A THEOREM:

GEOMETRY 4.3

CONGRUENCE of TRIANGLES is:

REFLEXIVE

SYMMETRIC, and

TRANSITIVE

A THEOREM:

GEOMETRY 4.3

GEOMETRY 4.3

GEOMETRY 4.3

GEOMETRY 4.3

GEOMETRY 4.3

GEOMETRY 4.3

GEOMETRY 4.3

B. COORDINATE GEOMETRY The vertices of ΔRST are R(–3, 0), S(0, 5), and T(1, 1). The vertices of ΔRST are R(3, 0), S(0, –5), and T(–1, –1). Use the Distance Formula to verify that corresponding sides are congruent. Name the congruence transformation for ΔRST and ΔRST.

GEOMETRY 4.3

You should be able to:

State the CPCTC Theorem

DESCRIBE how Triangle Congruence is Reflexive, Symmetric and Transitive

Use CPCTC in a Proof

DETERMINE if Corresponding Part of Triangles are Congruent.

GEOMETRY 4.4

Recall that CONGRUENCE means

o Same SHAPEo Same SIZE

GEOMETRY 4.4

Recall that CONGRUENCE means

o Same SHAPEo Same SIZE

Now for some SHORTCUT postulates and theoremsthat don’t require proving ALL Corresponding Angles and ALL Corresponding Sides are Congruent.

GEOMETRY 4.4

SSS Postulate

If the SIDES of one triangle are CONGRUENT to the SIDES of a Second Triangle,

THEN

the Triangles are CONGRUENT.

GEOMETRY 4.4

DEFINITION:

The Included Angle of Two Sides is the Angleformed by them.

A B

C

1

2

3

GEOMETRY 4.4

SAS Postulate

If TWO SIDES and the INCLUDED ANGLE of one Triangle are CONGRUENT to

TWO SIDES and the INCLUDED ANGLE of another Triangle

THEN

The Triangles are CONGRUENT.

GEOMETRY 4.4

GEOMETRY 4.4

GEOMETRY 4.4Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4Which pair of Triangles are CONGRUENT?

GEOMETRY 4.4

GEOMETRY 4.4