Question

Penny knows that point W is in the interior of XYZ. Based on this information, she claims that XYW = WYZ. Is Penny's claim necessarily true? Explain

A) Yes, Penny's claim is always true.
B) No, Penny's claim is not necessarily true.
C) Penny's claim is true only if X and Z are equal.
D) Penny's claim is true only if Y is the midpoint of XZ.

Answer 1

Penny's claim is not necessarily true. The angles XYW and WYZ cannot be assumed to be equal unless we have additional information about the triangle XYZ.

Step-by-step explanation:

Penny's claim is not necessarily true. In order to determine whether XYW is equal to WYZ, we need to examine the angles formed by those segments. If point W is in the interior of triangle XYZ, it means that it is not on any of the sides of the triangle. Therefore, we cannot assume that the angles XYW and WYZ are equal, unless we have additional information about the triangle.

If Penny's claim were true, it would imply that all interior angles of a triangle are equal, which is not the case. In a triangle, the sum of all interior angles is always 180 degrees, but each individual angle can be different. So, Penny's claim is not necessarily true.