Chapter 4.5, Problem 1WE

To determine

To find: the missing statements and reasons.

Explanation of Solution

Given information:

Given figure,

Given,

$\angle W$ and $\angle Y$ are right angles,

  $\overline{WX}\cong \overline{YX}$

Prove: $\overline{WZ}\cong \overline{YZ}$

Proof:

Given statements:

Statements	Reasons
1. $\angle W$ and   $\angle Y$ are right angles
2. $\Delta XWZ$ and   $\Delta XYZ$ are right angle triangle
3. $\overline{WX}\cong \overline{YX}$
	Reflexive property
5. $\Delta XWZ\cong --$

Calculation:

Given,

$\angle W$ and $\angle Y$ are right angles,

  $\overline{WX}\cong \overline{YX}$

Prove: $\overline{WZ}\cong \overline{YZ}$

The two columns proof is stated below:

Statements	Reasons
1. $\angle W$ and   $\angle Y$ are right angles	Given
2. $\Delta XWZ$ and   $\Delta XYZ$ are right angle triangle	According to the property of right angled triangle
3. $\overline{WX}\cong \overline{YX}$	Given
	Reflexive property
5. $\Delta XWZ\cong \Delta XYZ$	By the hypotenuses and legg methos
6. $\overline{WZ}\cong \overline{YZ}$	By CPCT