Question

The triangles shown below must be congruent.

Answer 1

True by the angle angle side theorem.

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.

Answer 2

Option A is correct.

Yes, it is true that the triangles shown are congruent.

Explanation:

Labelled the diagram as shown below in the attachment:

In triangle ABC and triangle PQR

`\angle ABC \cong \angle PQR = 90^(\circ)` [Angle]

`\angle ACB \cong \angle QPR = 40^(\circ)` [Angle]

`AC \cong PR = 12` units [Side]

AAS(Angle-Angle-Side) postulates states that the two angles and the non- included side of one triangle are congruent to the two angles and the non-included side of the other triangle., then the triangles are congruent.

Then, by AAS

`\triangle ABC \cong \triangle PQR`

Therefore, the given triangles shown must be congruent.