Question

. In the adjacent Figure 5.42, if
seg AB || seg PQ , seg AB seg PQ,
seg AC || seg PR, seg AC seg PR
then prove that,
seg BC || seg QR and seg BC 3 seg QR.
B
R
Fig. 5.42​

Answer 1

Step-by-step explanation:

Given: seg AB∥ seg PQ, seg AB≅segPQ

So, ABQP is a parallelogram as the pair of opposite sides are congruent and parallel.

Thus, seg AP ∥ seg BQ, seg AP≅segBQ …..(1)

Similarly, seg AC∥ seg PR,segAC≅segPR

So, APRC is a parallelogram.

Thus, seg AP∥segCR,segAP≅segCR…..(2)

From ( 1 ) and (2) we have

seg BQ∥ seg CR

Also, seg BQ≅segCR

Thus, BQRC is a parallelogram as the pair of opposite sides are congruent and parallel.

Therefore, seg BC∥ seg QR and segBC≅segQR as BQRC is a parallelogram.