Question

in the figure below, triangle abc is rotated 180° about point p to become triangle def. select the true statement. a. angles abc and dfe are congruent. b. angles bac and dfe are congruent. c. angles bac and def are congruent. d. angles abc and def are congruent.

Explanation:

Step1: Recall rotation property

A 180 - degree rotation is a rigid transformation. Rigid transformations (rotations, translations, reflections) preserve angle - measure and side - length.

Step2: Identify corresponding angles

When \(\triangle ABC\) is rotated 180° about point \(P\) to form \(\triangle DEF\), the corresponding angles are congruent. The order of the vertices in the triangle names gives the corresponding angles. Angle \(ABC\) corresponds to angle \(DEF\), angle \(BAC\) corresponds to angle \(EDF\), and angle \(ACB\) corresponds to angle \(DFE\). So, angles \(ABC\) and \(DEF\) are congruent.

Answer:

D. Angles ABC and DEF are congruent.