Exercise 4

Chapter 9, Section 9-1, Page 387
enVision Geometry 1st Edition by Al Cuoco
ISBN: 9780328931583

Solution

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(a)\textbf{(a)}

The figure appears to be a kite. A kite has two pairs of consecutive congruent sides and no opposite sides congruent. Use the Distance Formula to find the lengths of the sides:

PQ=(22)2+(51)2=0+16=16=4QR=(72)2+(65)2=25+1=26RS=(67)2+(16)2=1+25=26PS=(62)2+(11)2=16+0=16=4\begin{align*} PQ&=\sqrt{(2-2)^2+(5-1)^2}=\sqrt{0+16}=\sqrt{16}=4\\ QR&=\sqrt{(7-2)^2+(6-5)^2}=\sqrt{25+1}=\sqrt{26}\\ RS&=\sqrt{(6-7)^2+(1-6)^2}=\sqrt{1+25}=\sqrt{26}\\ PS&=\sqrt{(6-2)^2+(1-1)^2}=\sqrt{16+0}=\sqrt{16}=4 \end{align*}

Consecutive pair QR\overline{QR} and RS\overline{RS} and consecutive pair PQ\overline{PQ} and PS\overline{PS} are congruent. No opposite pair is congruent, so PQRSPQRS is a kite.\text{\color{#c34632}{kite.}}

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