Question

which postulate would prove these two triangles are congruent?

neither
sss
sas

Explanation:

Identify the given congruent parts

The markings on the two triangles show:

• One pair of sides with double tick marks is congruent.
• Another pair of sides with single tick marks is congruent.
• One pair of angles with single arc marks is congruent.

Analyze the vertical angles

Using the Vertical Angles knowledge point

$$ \text{The vertical angles at the intersection are congruent.} $$

Determine the congruence postulate

We have two congruent sides and an angle. However, the congruent angle marked with the arc is adjacent to the side with the single tick mark, but it is not the included angle between the two marked sides. The vertical angles at the intersection are also not the included angles between the marked sides.

For the SAS (Side-Angle-Side) postulate to apply, the congruent angle must be strictly between the two congruent sides. Since the marked congruent angle is not the included angle, we do not have enough information to prove congruence.

Select the correct option

Since SSS and SAS do not apply, the correct choice is "Neither".

Answer:

• (A) Neither (Correct answer)
• (B) SSS
• (C) SAS