Question

triangle congruence theorems
sss (side-side-side)
aas (angle-angle-side)
sas (side-angle-side)
asa (angle-side-angle)
hl (hypotenuse-leg)
multiple-choice question
which of the following is the correct statements for the pair of adjacent angles that are shown to
be congruent in the aas image?
∠a ≅ ∠d
∠b ≅ ∠f
∠a ≅ ∠d
∠c ≅ ∠f
∠a ≅ ∠d
∠b ≅ ∠e
∠c ≅ ∠f
∠a ≅ ∠d
∠b ≅ ∠e

Explanation:

Step1: Recall AAS (Angle - Angle - Side) theorem

AAS states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Step2: Analyze the given options

In the AAS image, we need to check the angle congruences. The AAS theorem requires two pairs of congruent angles.

• For the AAS (Angle - Angle - Side) congruence criterion, we have \(\angle A\cong\angle D\) (one pair of angles) and \(\angle B\cong\angle E\) (another pair of angles) as per the AAS triangle congruence setup shown in the image.

Answer:

\(\angle A\cong\angle D\) and \(\angle B\cong\angle E\)