Question

A transversal EF of line AB and line CD intersects the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisectors of angle BPQ AND ANGLE PQC respectively. prove that line AB parallel to line CD.

Answer 1

Line PR ll Line QS
Consider Seg EF as transversal

ĽRPQ =ĽPQS. . . (Alternate angles) . . . 1


But Ray PR and Ray QS are angle bisectors of angle BPQ and PQC respectively

ĽBPR=ĽRPQ. . . . . 2

ĽPQS=ĽSQF. . . . . 3
Now,
ĽRPQ=ĽPQS
... ĽBPR=ĽSQF. . . . Substituting from 2&3. . . .(4)


Add 1&4
ĽRPQ+ĽBPR=ĽPQS+ĽSQF

ĽBPQ=ĽPQS. . . . . (Angle addition property) .

But above angles are alternate angles for line AB & lineCD

... Line AB ll Line CD. . . . (Alternate angle tsst)

Answer 2

Answer:

Step-by-step explanation:

line PR || line QS

Consider seg EF as transversal /_ RPQ = /_ PQS