Question

Given: X is the midpoint of WY, WX = XZ Prove: XY = XZ

Answer 1

Answer with explanation:

According to the given question we have ,

Given : X is the midpoint of WY,  $\overline{WX}\cong\overline{XZ}$

To prove : $\overline{XY}\cong\overline{XZ}$

Proof :   Statement              Reasons.

1. X is the midpoint of WY 1. Given

2. WX= XY                       2. Midpoint divides line segment into equal halves.                                      

3. $\overline{WX}\cong\overline{XZ}$                        3. Given

4. WX= XZ                      4. Congruent segments are equal.

5. XY = XZ                        5. Transitive property of equality .(using (2) and (4))

6.  $\overline{XY}\cong\overline{XZ}$  6. Equal line segments are congruent.

Important points :

• Transitive property equality says that if a= b and b=c then a=c , where a, b and c be any real number.
• Midpoint of an line segment into equal halves.                                      
• Congruent line segments are equal in lengths.
• Equal line segments are congruent.

Answer 2

Answer:

proved XY=XZ

Step-by-step explanation:

As it is given that X is the mid point of WY, it means,

WX=XY-----(1)

Also it is given in the statement that

WX=XZ-----(2)

On equating equation 1 and 2 we have,

XY=XZ