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 base angles of the gable have a sum of 180°. b. the length of the horizontal side of the gable is equal to the sum of the lengths of the two diagonal sides. 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:

An isosceles triangle has a key property: the angles opposite its two congruent sides (the base angles) are congruent.

• For option A: The sum of all three angles in any triangle is $180^\circ$, so the sum of just the two base angles must be less than $180^\circ$, making this false.
• For option B: The triangle inequality theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides, so this is false.
• For option C: There is no rule that the base of an isosceles triangle is half the sum of the other two sides; this does not hold for most isosceles triangles, making this false.
• For option D: This matches the core property of isosceles triangles, so it is true.

Answer:

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