#### Exercise 4

Chapter 9, Section 9-1, Page 387

ISBN: 9780328931583

Solution

VerifiedStep 1

1 of 3$\textbf{(a)}$

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:

$\begin{align*} PQ&=\sqrt{(2-2)^2+(5-1)^2}=\sqrt{0+16}=\sqrt{16}=4\\ QR&=\sqrt{(7-2)^2+(6-5)^2}=\sqrt{25+1}=\sqrt{26}\\ RS&=\sqrt{(6-7)^2+(1-6)^2}=\sqrt{1+25}=\sqrt{26}\\ PS&=\sqrt{(6-2)^2+(1-1)^2}=\sqrt{16+0}=\sqrt{16}=4 \end{align*}$

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

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