Question

At an art supply store, two different triangular rulers are available. One has angles 45°, 45°, and 90°. The other has angles 30°, 60°, and 90°. Which triangle is isosceles?

a) The triangle with angles 45°, 45°, and 90°
b) The triangle with angles 30°, 60°, and 90°
c) Both triangles are isosceles
d) Neither triangle is isosceles

Answer 1

The isosceles triangle has angles measuring 45°, 45°, and 90°, where the two 45° angles indicate two equal sides, making it an isosceles right triangle. The triangle with angles of 30°, 60°, and 90° is not isosceles but a special right triangle.

Step-by-step explanation:

The triangle that is isosceles is the one with angles measuring 45°, 45°, and 90°. An isosceles triangle is defined as a triangle with at least two sides of equal length. Since a triangle with two 45° angles must have those two sides opposite of those angles being the same length, it is considered isosceles. The 90° angle indicates that it is also a right angle triangle, often referred to as an isosceles right triangle.

On the other hand, a triangle with angles of 30°, 60°, and 90° is not isosceles as it has no two sides that are the same length; instead, this type of triangle is known as a 30-60-90 triangle, which is a special type of right triangle.

Therefore, the answer to which triangle is isosceles is (a) The triangle with angles 45°, 45°, and 90°.