Question

question 8 of 10
a right triangle with two congruent legs is always a 45 - 45 - 90 triangle.
a. true
b. false

Explanation:

In a right triangle, if two legs are congruent (equal in length), the two acute angles opposite those legs must be equal (by the Isosceles Triangle Theorem, which states that if two sides of a triangle are equal, the angles opposite them are equal). The sum of the acute angles in a right triangle is \( 90^\circ \) (since the total sum of angles in a triangle is \( 180^\circ \), and one angle is \( 90^\circ \) for a right triangle). Let each acute angle be \( x \). Then \( x + x + 90^\circ= 180^\circ \), which simplifies to \( 2x = 90^\circ \), so \( x = 45^\circ \). Thus, the angles of the triangle are \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \), making it a 45 - 45 - 90 triangle.

Answer:

A. True