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Chapter 14: Q18. (page 580)

In Exercise 18-20, refer to the diagrams on page 578. Given the reflection Rm:PQ鈫�鈫�P'Q'鈫�, write the key steps of a proof that PQ=P'Q'for each case.

Case 2.

Short Answer

Expert verified

The required proof is as shown in the below steps.

Step by step solution

01

Step 1. Given Information.

Given the reflection Rm=PQ炉鈫�P'Q'炉 and the diagram,

02

Step 2. Formula Used.

Definition of reflection.

03

Step 3. Proof.

In the given reflection through m P=P'

And Q has a reflection Q'so from the definition of reflection we know that QQ'炉鈯�m and, Q and Q'are equidistance from line m, and let O be the intersection of QQ'炉 and m.

Here

PO is common, 鈭�POQ=鈭�POQ'and OQ=OQ'

Hence 螖POQ=~螖POQ'.

Now as the triangle are congruent, it can be concluded that PQ=P'Q'.

Therefore, PQ=P'Q' is proved.

04

Step 4. Conclusion.

It is proved that, PQ=P'Q'.

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