Congruent Figures LESSON 4-1 Additional Examples

ABC QTJ

. List the congruent corresponding parts.

List the corresponding vertices in the same order. Angles: 

A



Q



B



T



C



J

List the corresponding sides in the same order.

Sides:

AB QT BC TJ AC QJ

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Congruent Figures LESSON 4-1 Additional Examples

XYZ KLM

,

m



Y

= 67, and

m



M

= 48. Find

m



X

.

Use the Triangle Angle-Sum Theorem and the definition of congruent polygons to find

m



X

.

m



X + m



Y + m



Z

= 180

m



Z

=

m



M

Triangle Angle-Sum Theorem Corresponding angles of congruent triangles that are congruent Substitute 48 for

m



M.

m



Z

= 48

m



X

+ 67 + 48 = 180

m



X

+ 115 = 180

m



X

= 65 Substitute.

Simplify.

Subtract 115 from each side.

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Congruent Figures LESSON 4-1 Additional Examples

Can you conclude that

ABC CDE

in the figure below?

List corresponding vertices in the same order.

If

ABC CDE

, then 

BAC

The diagram above shows 

BAC



DCE.



DEC

, not 

DCE

.

Corresponding angles are not necessarily congruent, therefore you

cannot

conclude that

ABC CDE

.

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Congruent Figures LESSON 4-1 Additional Examples

Given: CG DG, CN DN

, 

C

are right angles.

Prove: CNG DNG.



D,



CNG

and 

DNG

a.

CG DG

Congruent triangles have three congruent corresponding sides and three congruent corresponding angles.

Examine the diagram, and list the congruent corresponding parts for

CNG

and

DNG

.

Given b.

CN DN

Given c.

GN GN

Reflexive Property of Congruence d. 

C

e. 

CNG



D

f. 

CGN

Given 

DNG

Right angles are congruent.



DGN

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. (Theorem 4-1.) g.

CNG DNG

Definition of triangles

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