Question

in the model of a house, the front - facing gable at the end of the roof forms an isosceles triangle where the diagonal sides of the gable are congruent in length
which statement is true?
a. the length of the horizontal side of the gable is equal to the sum of the lengths of the two diagonal sides.
b. the base angles of the gable have a sum of 180°.
c. the length of the horizontal side of the gable is half the length of the sum of the two diagonal sides.
d. the base angles of the gable are also congruent

Explanation:

Step1: Analyze option A

By triangle inequality, the sum of two sides of a triangle is greater than the third side. So the length of the horizontal side (base) of the isosceles triangle (gable) is not equal to the sum of the two diagonal sides.

Step2: Analyze option B

The sum of all three angles of a triangle is \(180^{\circ}\). In an isosceles triangle, the sum of the base angles is \(180^{\circ}-\text{vertex angle}
eq180^{\circ}\)

Step3: Analyze option C

There is no such property that the length of the base of an isosceles triangle is half the sum of the two equal - side lengths.

Step4: Analyze option D

In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent. This is a fundamental property of isosceles triangles.

Answer:

D. The base angles of the gable are also congruent.