Question

brooke wants to prove that in the figure shown, \\( \triangle pqt \\) is congruent to \\( \triangle rst \\) using the side - angle - side postulate. in brookes proof, which statement would give the justification to show that the included angles are congruent? \\( \bigcirc \\) right angles are congruent. \\( \bigcirc \\) vertical angles are congruent. \\( \bigcirc \\) alternate interior angles are congruent. \\( \bigcirc \\) alternate exterior angles are congruent.

Explanation:

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures. In the context of proving triangle congruence using the Side - Angle - Side (SAS) postulate, if we can show that the included angles (the angles between two pairs of corresponding sides) are congruent, vertical angles (which are congruent by their property) can serve as that included angle justification. Alternate interior/exterior angles are related to parallel lines and transversals (not indicated here as a parallel - line context). Right angles would need a right - angle indicator (not shown).

Answer:

Vertical angles are congruent.