Question

Which rule explains why these triangles are congruent?

A. SAS
B. ASA
C. AAS
D. These triangles cannot be proven congruent.

Answer 1

The rule that explains why the two triangles are congruent is the Angle-Angle-Side (AAS) congruence theorem:

• C. AAS

Explanation:

According to the Vertical Angle Theorem, opposite vertical angles of two straight intersecting lines are congruent. Therefore:

• m∠NHM = m∠KHJ

From inspection of the triangles:

• m∠N = m∠K
• 
  `\sf \overline{MH}=\overline{JH}`

Therefore, triangle NHM and triangle KHJ have two congruent angles and one congruent side. As the side is not included between the two angles, the rule that explains that the triangles are congruent is AAS.

Angle-Angle-Side (AAS) Congruence Theorem

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.