Two right triangles are similar if an acute angle of one triangle is congruent to an acute angle of the other triangle.A.TrueB.FalseSUBMITarrow_backPREVIOUS

Answer

The statement is True.

Detailed Explanation

1. Definition of Similar Triangles: Two triangles are considered similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

2. Acute Angles: In right triangles, one angle is always 90 degrees (the right angle), and the other two angles are acute. Thus, if one acute angle of the first triangle is congruent to an acute angle of the second triangle, this establishes that at least one pair of corresponding angles are equal.

3. Using Angle-Angle (AA) Criterion: The Angle-Angle criterion for triangle similarity states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar. Since one angle is the right angle (90 degrees) and the other two angles are acute, the congruence of one pair of acute angles ensures similarity.

Therefore, since one acute angle matches in both triangles, we can conclude that they are similar based on the properties of triangles. Thus, option A is the correct choice.