Proving RightTriangles

Congruent

Proving RightTriangles

Congruent

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Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

How much do you How much do you need to know. . .need to know. . .

. . . about two triangles to prove that they are congruent?

In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

Corresponding PartsCorresponding Parts

ABC DEF

B

A

C

E

D

F

1. AB DE

2. BC EF

3. AC DF

4. A D

5. B E

6. C F

Do you need Do you need all six ?all six ?

NO !

SSSSASASAAAS

Do you need to use these Do you need to use these for right trianglesfor right triangles ? ?

NO !

HLHALLLA

Right triangle vocabulary

Leg hypotenuse

legSince you know the right angles always match

you only need two more parts to be congruent.

LL : leg - leg

LA : leg - angle

HA : hypotenuse - angle

HL : hypotenuse - leg

Name That PostulateName That Postulate(when possible)

Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

B D

For AAS: A F

AC FE

HWHWIndicate the additional information needed to enable us to apply the specified congruence postulate.

For LA:

For LL:

A

CB

D

FE