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Congruent Triangles

Lesson 4.3

by Marty R., Shanon V., Vilma V.

Standard 5

OBJECTIVE

Use properties of congruent triangles. Prove

triangles congruent by using the definition of

congruence.

Vocabulary

Congruent - a correspondence between their angles

and sides. Corresponding Angles - Two angles that

are formed by two lines and a transversal and

occupy corresponding positions. Corresponding

Sides - When two figures are congruent the sides

that are in corresponding positions are congruent.

How are triangles congruent? They are congruent

when each pair of the triangles corresponding

sides are equal, or congruent, and the

corresponding angles are congruent too.

Properties of Congruent Triangles

Reflexive Property of Congruent Triangles Every

triangle is congruent to itself. Symmetric

Property of Congruent Triangles If ?ABC ? ?DEF,

then ?DEF ??ABC. Transitive Property of Congruent

Triangles If ?ABC??DEF and ?DEF??JKL, then

?ABC??JKL.

K

L

J

Third Angles Theorem

If two angles of one triangle, then the third

angles are also congruent. If LA?LD and LB? LE,

then LC? LF.

B

E

D

F

C

A

Note the Triangle Sum Theorem states that all

triangles equal 180 degrees.

Using the Third Angle Theorem

Find x.

In the diagram, LN? LR and LL? LS. From the Third

Angles Theorem, you know that LM? LT. So, mLM?

mLT. From the Triangle Sum Theorem, mLM

180-50-65 60.

mLMmLT 60(2x30) 302x 15x

Third Angle Theorem

T

R

M

Substitute.

Subtract three from each side.

N

L

S

Divide each side by 2.

Classwork

GREENBOOK/pg. 234 1-10

Homework

GREENBOOK/pg. 235 13-19

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