Question

1. an isosceles triangle has two sides of equal length. if the base angles are 45° each, what type of isosceles triangle is it?

equiangular
acute isosceles
equilateral
right isosceles

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the vertex angle

Let the vertex angle be \(x\). The base angles are \(45^\circ\) each. So, \(x + 45^\circ+ 45^\circ = 180^\circ\). Solving, \(x = 180^\circ - 90^\circ = 90^\circ\).

Step3: Identify the triangle type

Since one angle is \(90^\circ\) and two sides are equal (isosceles), it is a right isosceles triangle.

Answer:

D. Right Isosceles (assuming the options are labeled with D for the last option as per the standard multiple - choice layout here, with the last option being "Right Isosceles")