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

This is about line theorems.

The reasons are;

1) Given

2) Midpoint divides a line into two equal parts

3) Transitive Property of Inequality.

4) Congruent sides are equal

5) Transitive Property of Inequality

6) Equal sides are congruent

From the given image, we see that the line XZ is perpendicular to WY.

1)  X is the midpoint of WY;  This is given in the question already.

2) WX = XY; This is because the midpoint of a line divides that line into two equal parts.                                    

3. WX ≅ XZ; This is as a result of transitive property of equality which states that if x = y and y = z, then x = z. This means that WX is congruent to XZ and therefore equal to XZ.

4. WX = XZ; As said in point 3 above that congruent means equal.

5. XY = XZ; This is as a result of transitive property of equality which states that if x = y and y = z, then x = z.

6. XY ≅ XZ; As stated earlier, equal sides are congruent.

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