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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.
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
To identify the corresponding sides and angles of the congruent trapezoids, we can compare the given information about each trapezoid.
Given trapezoid A B C D:
- Corresponding sides:
- Side A B corresponds to side R S.
- Side C D corresponds to side P Q.
- Corresponding angles:
- Angle B is adjacent to the shorter parallel side in A B C D. It corresponds to angle S, which is adjacent to the shorter parallel side in R S P Q.
- Angle C is adjacent to the longer parallel side in A B C D. It corresponds to angle P, which is adjacent to the longer parallel side in R S P Q.
- Angle A in A B C D corresponds to angle R in R S P Q.
- Angle D in A B C D corresponds to angle Q in R S P Q.
Therefore, the corresponding sides and angles of the congruent trapezoids are as follows:
- Corresponding sides:
- Side A B corresponds to side R S.
- Side B C corresponds to side S R.
- Side C D corresponds to side P Q.
- Side D A corresponds to side Q R.
- 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.