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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

Since the two trapezoids are congruent, their corresponding angles and sides are equal in measure.

Corresponding sides:
- Side AB corresponds to side PQ
- Side BC corresponds to side SR
- Side CD corresponds to side PQ
- Side AD corresponds to side RS

Corresponding angles:
- Angle A corresponds to angle R
- Angle B corresponds to angle S
- Angle C corresponds to angle P
- Angle D corresponds to angle Q