Question

A triangle, ABC, has angle measures of 45°, 45°, and 90° and two congruent (equal) sides. How would this triangle be classified?

O Isosceles acute
O Scalene acute
O Scalene right
O Isosceles right

Answer 1

(d) Isosceles right

Explanation:

You want to know the classification of a triangle with angles 45°-45°-90°.

Classification

The largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.

Two of the angles have the same measure. This means the triangle is an isosceles triangle.

The triangle is classified as an isosceles right triangle.

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Additional comment

A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.

If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.

Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.

It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.