Chapter 4 – Congruent Triangles

4-1 Congruent Figures

Objective: Recognize congruent figures and their corresponding parts.

DEF ≅ GHI

Vocabulary

are figures that have the same size and shape.

(DNG pages 72-74, text reference pages 198-200) 4-1 Congruent Figures

When you name congruent polygons, always list corresponding vertices in the same order.

Congruent polygons have congruent corresponding parts

Matching vertices are corresponding vertices.

Matching sides are corresponding sides.

Matching angles are corresponding angles.

Congruent polygons

When two figures are congruent, you can move one so that it fits exactly on the other one.

T C

180

QJ BC

mM

65

48

48 67

115

Examples

Examples

ABC

DCE

DEC is not

DC DE EC

CDE DEC

ACB

EDC

35

YSW K VM WYS MKV SWY VMK

No, corresponding sides are not congruent.

Practice 4-1 Congruent Figures

Each pair of polygons is congruent. Find the measures of the numbered angles.

CAT ≅ JSD. List each of the following.

4. three pairs of congruent sides

5. three pairs of congruent angles

m1 = 110, m2 = 120 m3 = 90, m4 = 135 m5 = 140, m6 = 90,

m7 = 40, m8 = 90

C ≅ J , A≅ S , T ≅ D

(DNG page 317)

Practice 4-1 Congruent Figures

7. four pairs of congruent angles

6. four pairs of congruent sides

WXYZ ≅ JKLM. List each of the following.

State whether the pairs of figures are congruent. Explain.

W ≅ X X ≅ K Y ≅ L Z ≅ M

/

// //

////

GHJ ≅ IHJ

by Theorem 4-1

HJ ≅ HJ

by Reflexive Prop. of ≅,

GHJ ≅ IHJ

by the definition of ≅ triangles.

YES

X

RSQ ≅ VST

by Vertical s Theorem

QRS ≅ TSV

by Theorem 4-1

but none of the

sides are

necessarily ≅.

NO

(DNG page 317)

Practice 4-1 Congruent Figures

10. Developing Proof Use the information given in the diagram.

Give a reason that each statement is true.

Given

Vertical Angles Theorem

Theorem 4-1

Given

Definition of ≅ Triangles

(DNG page 317)