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The two figures shown above are congruent. Identify the corresponding sides and angles.
The photo description: 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.
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Corresponding sides:
- Side AB in trapezoid ABCD corresponds to side RS in trapezoid RSPQ.
- Side BC in trapezoid ABCD corresponds to side PQ in trapezoid RSPQ.
- Side CD in trapezoid ABCD corresponds to side SR in trapezoid RSPQ.
- Side AD in trapezoid ABCD corresponds to side RQ in trapezoid RSPQ.
Corresponding angles:
- Angle A in trapezoid ABCD corresponds to angle R in trapezoid RSPQ.
- Angle B in trapezoid ABCD corresponds to angle S in trapezoid RSPQ.
- Angle C in trapezoid ABCD corresponds to angle P in trapezoid RSPQ.
- Angle D in trapezoid ABCD corresponds to angle Q in trapezoid RSPQ.
Corresponding sides and angles in congruent figures are the matching sides and angles in each figure. In this case, we have two trapezoids, Trapezoid ABCD and Trapezoid RSPQ. Let's identify the corresponding sides and angles.
Corresponding angles:
1. Angle B in Trapezoid ABCD corresponds to Angle S in Trapezoid RSPQ.
2. Angle C in Trapezoid ABCD corresponds to Angle P in Trapezoid RSPQ.
3. Angle A in Trapezoid ABCD corresponds to Angle R in Trapezoid RSPQ.
4. Angle D in Trapezoid ABCD corresponds to Angle Q in Trapezoid RSPQ.
Corresponding sides:
1. Side AB in Trapezoid ABCD corresponds to Side RS in Trapezoid RSPQ.
2. Side CD in Trapezoid ABCD corresponds to Side PQ in Trapezoid RSPQ.
3. Side AD in Trapezoid ABCD corresponds to Side RQ in Trapezoid RSPQ.
4. Side BC in Trapezoid ABCD corresponds to Side PS in Trapezoid RSPQ.
To summarize:
- Corresponding angles: B corresponds to S, C corresponds to P, A corresponds to R, and D corresponds to Q.
- Corresponding sides: AB corresponds to RS, CD corresponds to PQ, AD corresponds to RQ, and BC corresponds to PS.
I have identified the corresponding sides and angles between Trapezoid ABCD and Trapezoid RSPQ based on the given information.