Chapter 4.6, Problem 5WE

To determine

To prove: $\overline{DX}\cong \overline{EX}$ .

Explanation of Solution

Given Information:

Given figure,

  

Key steps of proof:

a. $\Delta POD\cong \Delta POE$

b. $\overline{PD}\cong \overline{PE}$

c. $\Delta PDX\cong \Delta PEX$

d. $\overline{DX}\cong \overline{EX}$

Calculation:

The key steps of the proof are:

1. $\Delta POD\cong \Delta POE$

Since one angle and two sides of one triangle are equal to one angle and two sides of another triangle.

Therefore, by side angle side congruency.

It is concluded that, two triangles are congruent.

2. $\overline{PD}\cong \overline{PE}$ (Corresponding parts of $\cong \Delta$ are $\cong$)
3. $\Delta PDX\cong \Delta PEX$ (HL postulate)
4. $\overline{DX}\cong \overline{EX}$ (Corresponding parts of $\cong \Delta$ are $\cong$)

Hence it is concluded that $\overline{DX}\cong \overline{EX}$ .