Chapter 12.2, Problem 9E

To determine

To find:

Thevalues of $x$ and $y$ .

Answer to Problem 9E

  $x=7$

  $y=8$ .

Explanation of Solution

Given:

  $ABCD\cong EFGH$

Concept used:

Two geometric figures are congruent if a rigid motion or a composition of rigid motions maps one of the figures onto other.

Calculation:

The pairs of congruent corresponding sides

  $\begin{array}{l}BC=FG\\ 135=10x+65\\ 70=10x\\ x=7\end{array}$

The pairs of congruent corresponding angles

  $\begin{array}{l}m\angle A=m\angle E\\ {28}^0={\left(4y-4\right)}^0\\ 32=4y\\ y=8\end{array}$

Therefore,

The values of $x=7$ and $y=8$ .