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GIVEN. ∠ RTQ RTS. 1 2 ,. QT ST. PROVE. If you can show that QRT SRT , you will know that QT ST. First, copy the diagram and mark the given. information. EXAMPLE 1. Use congruent triangles.

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GIVEN

∠ RTQ RTS

1 2,

QTST

PROVE

If you can show that QRT SRT, you will know that QT ST.

First, copy the diagram and mark the given

information.

EXAMPLE 1

Use congruent triangles

Explain how you can use the given information to prove that the hanglider parts are congruent.

SOLUTION


Mark given information.

Add deduced information.

Two angle pairs and a non-included side are congruent, so by the AAS Congruence Theorem, . Because corresponding parts of congruent triangles are congruent,

QRT SRT

QTST.

EXAMPLE 1

Use congruent triangles

Then add the information that you can deduce. In this case, RQT and RST are supplementary to congruent angles, so

∠ RQT RST. Also,

RTRT .


Explain how you can prove that

AC.

AB BC

Given

AD DC

Given

BD BD

Reflexive property

ANSWER

Thus the triangle by SSS

ABDBCD

for Example 1

GUIDED PRACTICE

SOLUTION


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