Question

1. triangles mno and rst are shown. which theorem could be used to prove that △ mno ≅ △ rst?

angle-side-angle (asa)
side-side-angle (ssa)
side-side-side (sss)
side-angle-side (sas)

Explanation:

To determine the congruence theorem for \(\triangle MNO\) and \(\triangle RST\), we analyze the markings:

1. ASA (Angle - Side - Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

• Looking at the triangles, we can see that there are two pairs of congruent angles (marked angles) and the included side (marked side) between them.
• SSA is not a valid congruence theorem (it does not guarantee triangle congruence in all cases).
• SSS requires three pairs of congruent sides, and from the diagram, we don't have enough side markings for SSS.
• SAS requires two sides and the included angle, but the markings here suggest two angles and the included side, which fits ASA.

Answer:

A. Angle - Side - Angle (ASA)