Question

a triangle, △ abc, has angle measures of 45°, 45°, and 90°, and two congruent (equal) sides. how would this triangle be classified?
scalene acute
isosceles acute
isosceles right
scalene right

Explanation:

Step1: Analyze angle type

The triangle has a \(90^\circ\) angle, so it's a right triangle.

Step2: Analyze side/congruent angles

It has two \(45^\circ\) angles (congruent), so the sides opposite these angles are congruent (isosceles property: equal angles \(\implies\) equal sides).

Step3: Classify the triangle

Combining right (from \(90^\circ\)) and isosceles (from two congruent sides/angles), it's an isosceles right triangle.

Answer:

Isosceles right (the option labeled "Isosceles right")