Question

Given: X is the midpoint of WY and VZ Prove: angle XWV is congruent to angle XYZ

Answer 1

`\Delta XWV\text{ and }\Delta XYZ\text{ are similar by SAS}`

Here, we want to prove that XWV and XYZ is similar

We proceed as follows;

1) WX = XZ; and VX = XZ

Reason; Given that X is the midpoint of WY and VZ

2) angle VXW and YXZ are equal

Reason; They are vertically opposite angles

Thus, we have two equal sides and an equal angle

The angle is between the two sides; this mean that the triangles are equal according to Side-Angle-Side (SAS)