Question

determine whether the pair of triangles is similar. explain your reasoning.

Explanation:

Step1: Identify given congruent angles

We know $\angle A = 87^\circ$, $\angle T = 87^\circ$, so $\angle A \cong \angle T$. Also, the marked angles $\angle C \cong \angle V$.

Step2: Apply AA similarity criterion

For two triangles, if two pairs of corresponding angles are congruent, the triangles are similar by the Angle-Angle (AA) Similarity Postulate.
In $\triangle ABC$ and $\triangle TUV$:
$\angle A \cong \angle T$, $\angle C \cong \angle V$, so the third pair of angles will also be congruent (since the sum of angles in a triangle is $180^\circ$: $\angle B = 180^\circ - 87^\circ - \angle C$, $\angle U = 180^\circ - 87^\circ - \angle V$, so $\angle B \cong \angle U$).

Answer:

The pair of triangles $\triangle ABC$ and $\triangle TUV$ are similar. This is confirmed by the AA (Angle-Angle) Similarity Postulate, as two pairs of corresponding angles are congruent ($\angle A \cong \angle T = 87^\circ$ and $\angle C \cong \angle V$), which guarantees the third pair of angles is also congruent, making the triangles similar.