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. this is all they gave me

Solution:

Description about Trapezoid A B CD

⇒∠B= ∠C=90°

⇒AB ║ CD

⇒∠A= Obtuse, ∠D= Acute

and, BC< AD< AB< CD

Description of Trapezoid R S P Q

⇒∠S=∠P=90°

⇒RS  ║ P Q

⇒∠R=Obtuse, ∠ Q= Acute

⇒SP< R Q< RS< P Q

It is given that two Trapezoids A B CD and R S P Q are congruent.

So,Corresponding Congruent Sides are

AB= RS, BC= SP, P Q= C D, AD= R Q

And , Corresponding angles which are equal in Trapezoids A B CD and RS P Q are

∠A= ∠R,

∠B=∠S=90°,

∠C=∠P=90°,

∠D=∠Q

In the trapezoids ABCD and RSPQ,

Angles A, B, C 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

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