Question

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

Explanation:

• Isosceles: Since the triangle has two congruent (equal) sides, it meets the definition of an isosceles triangle.
• Right - angled: As one of its angles is \(90^{\circ}\), it is a right - angled triangle.

Combining these two characteristics, the triangle is an isosceles right triangle.

• Scalene: A scalene triangle has all sides of different lengths. Since this triangle has two equal sides, it cannot be scalene.
• Acute: An acute triangle has all angles less than \(90^{\circ}\). Since this triangle has a \(90^{\circ}\) angle, it is not acute.

Answer:

Isosceles right