Answer :
Statements B), C), and E) could be true if ΔXWT is congruent to ΔYAQ, indicating that corresponding angles and sides are equal. Statement A) is always true as dilations change size and do not preserve congruency. Statement D) is false because specific transformations that preserve side lengths and angles are required for congruency.
When considering whether
ΔXWT is congruent to ΔYAQ, we must determine if transformations can map one triangle onto the other. According to classical geometry theorems, a transformation in the Euclidean plane that preserves distances and handedness can be expressed either as a translation or a rotation about some point. Moreover, angles and side lengths must also correspond between congruent triangles, so let’s address each statement individually:
(A) A dilation will not map one triangle onto the other as dilations change the size of the triangle.
(B) angle X is equal to angle Q if the triangles are congruent.
(C) WT is congruent to AQ if the triangles are congruent.
(D) Not any transformation will map one triangle onto the other; it must be specific transformations that preserve side lengths and angles.
(E) angle W is equal to angle A if the triangles are congruent.
Based on classical geometry, statements B), C), and E) are true only if the triangles are congruent. Statement A) is true since a dilation changes size, and statement D) is false because not all transformations preserve the necessary properties of congruent triangles.
