Question

which rule explains why these triangles are congruent? aas sss asa sas these triangles cannot be proven congruent.

Explanation:

1. Vertical Angles:

• \(\angle SPQ\) and \(\angle TPU\) are vertical angles. By the vertical - angles theorem, \(\angle SPQ=\angle TPU\).

1. Marked Sides:

• \(SP = UP\) (marked with two short lines) and \(QP = TP\) (marked with one short line).
• The Side - Angle - Side (SAS) congruence rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
• In \(\triangle SQP\) and \(\triangle TUP\), we have \(SP = UP\), \(\angle SPQ=\angle TPU\), and \(QP = TP\).

Answer:

SAS