Question

question
answer
quadrilateral abcd is a
it is a trapezoid because it has
, and it is isosceles because it has

Explanation:

Step1: Identify trapezoid property

A trapezoid has at least one pair of parallel sides. From the diagram, \( BC \parallel AD \) (marked with arrows), so it has one pair of parallel sides.

Step2: Identify isosceles trapezoid property

An isosceles trapezoid has legs (non - parallel sides) that are congruent. Here, \( AB = CD \) (marked with ticks), so the non - parallel sides are congruent. Also, in an isosceles trapezoid, base angles are equal. We know \( \angle B=115^{\circ} \), and \( \angle A = 180^{\circ}-\angle B=65^{\circ}\), \( \angle C=\angle B = 115^{\circ}\), \( \angle D=\angle A=65^{\circ}\) (since consecutive angles between parallel sides are supplementary and base angles are equal in isosceles trapezoid).

Answer:

Quadrilateral \(ABCD\) is a trapezoid (specifically an isosceles trapezoid). It is a trapezoid because it has one pair of parallel sides (\(BC\parallel AD\)), and it is isosceles because it has congruent non - parallel sides (\(AB = CD\)) (or because base angles are equal).