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Chapter 5: Q. 18 (page 199)

For the following figure, given that 鈻�PQRS;PA=RBthen prove thatAS=BQ .

Short Answer

Expert verified

Thus, the statement is AS=BQ.

Step by step solution

01

Step 1- Check the figure.

Consider the figure.

02

Step 2- Apply the SAS postulate.

SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

03

Step 3- Step description.

Consider the trianglesPAS and RBQ.

ConsiderPA=RB .

Use the definition of parallelogram such that

PS=RQ鈭�P=鈭�R

Use the SAS postulate that implies that 螖PAS鈮�螖RBQ.

As the corresponding parts of congruent triangles are congruent thus the sides are congruent such thatAS=BQ .

Therefore AS=BQ.

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