Question

show what you know
triangle rst and triangle wsx both have angle measures of 90° and 45°. what does this tell us about the two triangles?
the triangles are similar because two pairs of corresponding angles are congruent
the triangles are congruent because they share one angle
the triangles form a square when combined
the triangles are not similar because their sides lengths are different

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). For triangle \(RST\) with two angles \(90^{\circ}\) and \(45^{\circ}\), the third angle is \(180-(90 + 45)=45^{\circ}\). For triangle \(WSX\) with two angles \(90^{\circ}\) and \(45^{\circ}\), the third angle is \(180-(90 + 45)=45^{\circ}\).

Step2: Apply the AA (Angle - Angle) similarity criterion

The AA similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Here, two pairs of corresponding angles (\(90^{\circ}\) and \(45^{\circ}\)) are congruent.

Congruent triangles require all corresponding sides and angles to be equal. Just sharing one angle (or two angles) does not make them congruent. Also, two right - angled isosceles triangles (with angles \(90^{\circ},45^{\circ},45^{\circ}\)) combined form a square only if their side lengths are equal (but we are not given side - length information for congruence). Similarity of triangles is determined by angle - angle relationships, not by side - length differences (side - length ratios are for similarity ratios, but non - equal side lengths do not prevent similarity if angles are equal).

Answer:

The triangles are similar because two pairs of corresponding angles are congruent.