Question

if two right triangles each have a 45° angle, then the triangles must be—
equilateral
acute
similar
congruent

Explanation:

• Equilateral: A right - triangle cannot be equilateral because an equilateral triangle has all angles equal to \(60^{\circ}\), while a right - triangle has one angle equal to \(90^{\circ}\).
• Acute: An acute triangle has all angles less than \(90^{\circ}\). Since these are right - triangles (one angle is \(90^{\circ}\)), they are not acute.
• Similar: For two right - triangles, if one of the non - right angles is \(45^{\circ}\), then the third angle is \(180^{\circ}-90^{\circ}-45^{\circ}=45^{\circ}\) for both triangles. By the AA (angle - angle) similarity criterion (two angles of one triangle are equal to two angles of another triangle), the two right - triangles are similar.
• Congruent: Congruent triangles require all corresponding sides and angles to be equal. Just having the same set of angles (right angle and two \(45^{\circ}\) angles) does not guarantee that the sides are equal. The sides could be in proportion (for similarity) but not of the same length.

Answer:

C. similar