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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.

Question

Mathematics

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18 May, 11:04

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

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.

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Answers (1)

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Mauricio Alexander · Answer 1

AB = RS, BC = SP, CD = PQ, AD = RQ

m∠A = m∠R, m∠B = m∠S, m∠C = m∠P, m∠D = m∠Q

Step-by-step explanation:

∵ Trapezoid ABCD is congregant to trapezoid RSPQ

∴ AB = RS

∴ BC = SP

∴ CD = PQ

∴ AD = RQ

∴ m∠A = m∠R

∴ m∠B = m∠S = 90°

∴ m∠C = m∠P = 90°

∴ m∠D = m∠Q