Question

which postulate would prove these two triangles are congruent?
neither
asa
aas

Explanation:

Identify given geometric markings

We observe two triangles meeting at a central vertex.
The markings on the triangles indicate:

• One pair of congruent right angles (indicated by the square symbols).
• One pair of congruent vertical angles at the shared vertex (indicated by the single arc markings).
• One pair of congruent sides (indicated by the single tick marks).

Analyze the relative positions of the congruent parts

Using the Vertical Angles theorem, the angles sharing the central vertex are congruent.
For each triangle, we have:

• An angle (the right angle).
• An adjacent angle (the vertical angle).
• A non-included side (the side with the tick mark, which is opposite to the right angle).

Determine the congruence postulate

Using the Triangle Congruence Postulates, we match the pattern of congruent parts:

• Two angles and a non-included side are congruent.
• This corresponds to the Angle-Angle-Side (AAS) congruence theorem.

Answer:

• Neither
• ASA
• AAS (Correct answer)