4.6 Congruence in Right Triangles

You will construct and justify statement

about right triangles .

Lets start off with a definition.

The hypotenuse is the side opposite the right angle.

hypotenuse

The other two sides are called legs.

leg

Remember a right triangle has one right

angle.

If the hypotenuse and a leg of If the hypotenuse and a leg of a triangle are congruent to a triangle are congruent to the hypotenuse and leg on the hypotenuse and leg on another triangle, then the another triangle, then the

two triangles are congruent.two triangles are congruent.

Here comes a theoremHypotenuse-Leg Theorem

{HL}

BACBACEDFEDF

A

B

C D

E

F

Given: ADGiven: ADCB,CB,

D and D and B are right B are right ’’ss

Prove: Prove: ADCADCCBACBA

It’s time for a proof.

StatementStatement ReasonReason1. Given1. ADCB, D & B are rt

’s 2. Def of rt ’s2. ADC &CBA are rt ’s3. ACis hypotenuse 3. Def of hyp.

4. reflexive4. ACAC

A

D

B

C

5. ADCCBA 5. HL

AssignmentWorkbook

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