Question

The figure shows two right trapezoids. Trapezoid A B C D has right angles at B and C. Angle B is adjacent to the shorter parallel side. Angle C is adjacent to the longer parallel side. Angle A is obtuse. Angle D is acute. Sides A B and C D are parallel. The sides in order of length from shortest to longest are B C, A D, A B, and C D. Trapezoid R S P Q has right angles at S and P. Angle S is adjacent to the shorter parallel side. Angle P is adjacent to the longer parallel side. Angle R is obtuse. Angle Q is acute. Sides R S and P Q are parallel. The sides in order of length from shortest to longest are S R, R Q, R S, and P Q. The two figures shown above are congruent. Identify the corresponding sides and angles.

Answer 1

In the trapezoids ABCD and RSPQ,

Angles A, B, and D are corresponding to the angles R, S, P and Q respectively,

Also, the sides AB, BC, CD and DA are corresponding to the sides RS, SP, PQ and QR respectively.

Since, when two figures are congruent to each other then their corresponding sides and angles are also congruent.

Here, trapezoids ABCD and RSPQ are congruent.

Therefore, AB≅RS, AB≅RS, AB≅RS, AB≅RS

And, ∠A ≅ ∠R, ∠B ≅∠S, ∠C≅∠P, ∠D≅∠Q

Answer 2

∠B and ∠S, ∠A and ∠R, ∠C and ∠P, ∠D and ∠Q

BC and SR, AD and RQ, AB and RS, CD and PQ

Explanation:

Given two trapezoid ABCD and RSPQ

Trapezoid ABCD has right angles at B and C. Angle A is obtuse. Angle D is acute. Sides AB and CD are parallel. The sides in order of length from shortest to longest are BC, AD, AB, and CD.

Trapezoid RSPQ has right angles at S and P. Angle R is obtuse. Angle Q is acute. Sides RS and PQ are parallel. The sides in order of length from shortest to longest are SR, RQ, RS, and PQ.

Now, given above two trapezoid are congruent. We have to identify the corresponding sides and angles.

As given two right angles and obtuse and acute angle in both the trapezoid therefore, the corresponding angles we take from both according to given information are

∠B and ∠S, ∠A and ∠R, ∠C and ∠P, ∠D and ∠Q

Also, In trapezoid ABCD, BC<AD<AB<CD

In trapezoid RSPQ, SR<RQ<RS<PQ

∴ According to above given order the corresponding sides are

BC and SR, AD and RQ, AB and RS, CD and PQ