Chapter 4.6, Problem 2CE

To determine

To prove: the angle $\overline{AX}\cong \overline{DY}$ with the help of given information.

Answer to Problem 2CE

It is concluded that $\overline{AX}\cong \overline{DY}$ is proved.

Explanation of Solution

Given information:

The system information:

  $\text{Δ}PAL\cong \text{Δ}KAN$

  $\angle L\cong \angle N$

  $△LAX=△NAY$

Given image:

  

Calculation:

Key steps of proof are as follows:

  $\text{Δ}PAL\cong \text{Δ}KAN$ (Side-Angle-Side Postulate)

  $\angle PAL=\angle KAN$ Because they are adjacent angles

b. $\angle L\cong \angle N$ (Corresponding $\angle \text{s}$ of $\cong \text{Δs}$ are $\cong )$

c. $△LAX=△NAY$ (Angle -Side - Angle postulate)

  $\angle LAX=\angle NAY$ Because they are adjacent angles

d. $\overline{AX}\cong \overline{DY}$ (Corresponding parts of $\cong \text{Δs}$ are $\cong )$

Hence, $\overline{AX}\cong \overline{DY}$ is proved.