Question

Trapezoid EFGH and QRST are congruent.

1. What is the length of side QR?
2. Which angle in QRST corresponds to $\angle \mathrm{H}$?
3. What is the perimeter of QRST?

Answer 1

Step 1: Find the length of side QR.

Given, figure

From the given congruent figure, as we know corresponding parts of congruent figures are equal.

So, $\mathrm{QR}=\mathrm{EF}=3\mathrm{feet}$.

Step 2: Find the corresponds angle to $\angle \mathrm{H}$.

From the congruent figures, we can say that

The angle corresponds to $\angle \mathrm{H}$ is $\angle \mathrm{T}$.

Step 3: Find the perimeters of QRST.

From the given congruent figures, corresponding parts of congruent figures are equal.

So,

$$\begin{gathered} \Rightarrow \mathrm{EF}=\mathrm{QR}=3\mathrm{ft}. \\ \Rightarrow \mathrm{FG}=\mathrm{RS}=5\mathrm{ft}. \\ \Rightarrow \mathrm{GH}=\mathrm{ST}=4\mathrm{ft}. \\ \Rightarrow \mathrm{HE}=\mathrm{TQ}=8\mathrm{ft}. \end{gathered}$$

We know that perimeter of QRST=$\mathrm{QR}+\mathrm{RS}+\mathrm{ST}+\mathrm{TQ}$

So, $$\begin{gathered} 3+5+4+8 \\ =20\mathrm{ft}. \end{gathered}$$

Step 4: Final answer.

Hence, the perimeter of QRST is $20\mathrm{ft}.$