Question

Which shows two triangles that are congruent by AAS?

Answer 1

The last one, as shown in the attached picture.

Further explanation

• The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
• The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.
• The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
• The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.

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Notes

• The angle-side-side postulate for the congruent triangles doesn't exist because an angle and two sides don't guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non-included angle, then triangles don't seem to be necessarily congruent. This can be why there's no side-side-angle (SSA) and there's no angle-side- side postulate.
• The AAA (angle-angle-angle) postulate for congruent triangles does not work because having three corresponding angles of equal size is not enough to prove congruence. This principle is usually used for the similarity of two triangles.

Learn more

1. Which shows two triangles that are congruent by ASA? brainly.com/question/8876876
2. About vertical and supplementary angles  brainly.com/question/13096411  
3. Calculate the measures of the two angles in a right triangle brainly.com/question/4302397

Answer 2

The correct answer is:

The last one.

Explanation:

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

The only triangle in this list marked as having two congruent angles and a side that is not between them congruent is the last figure.