Question

brooke wants to prove that in the figure shown, △pqt is congruent to △rqs by the side - angle - side postulate. complete the statement brooke will use in her proof, to show the included angles are congruent. brooke writes ∠pqt = ∠rqs because vertical angles are congruent. corresponding angles are congruent. q is the midpoint of ps and rt. vertical angles are congruent. alternate interior angles are congruent.

Explanation:

Vertical angles are formed when two lines intersect. In the context of proving triangle - congruence by Side - Angle - Side (SAS), when two lines intersect at a point (such as lines RT and PS intersecting at Q in the triangles \(\triangle PQT\) and \(\triangle RQS\)), the non - adjacent angles formed (the vertical angles) are always congruent. This property helps in establishing the angle - part of the SAS congruence criterion.

Answer:

Vertical angles are congruent