Chapter 5.4, Problem 29WE

To determine

To show: $\angle 1\cong \angle 2$ and $\angle 1\cong \angle 3$

Answer to Problem 29WE

  $\angle 1\cong \angle 2$

  $\angle 1\cong \angle 3$

Explanation of Solution

Given information: $ABZY$ is a parallelogram,

  $\overline{AY}\cong \overline{BX}$

Proof:

In $\Delta AYZ$ and $\Delta ABZ$

$ZB\cong AB$	Sides of rhombus are equal
$\angle 1\cong \angle 3\left(1\right)$	Angles opposite to equal sides are equal
$AY\parallel BZ$ So, $\angle 1\cong \angle 4\left(2\right)$	Opposite side of rhombus are parallel and transversal $AZ$
From, $\left(1\right)$and $\left(2\right)$   $\angle 2\cong \angle 1$	Alternate angles

Therefore, $\angle 1\cong \angle 3$ and $\angle 1\cong \angle 2$ .