Question

ZP = ZQ and Z1 = Z2. Prove that
RT || PQ.

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Answer 1

Answer:

ZP+ZQ=Z1+Z2. (exterior angle theoram)

ZQ+ZQ=Z2+Z2(since ZQ andZP and Z1 angle Z2

are equal so replacing them)

2ZQ=2Z2

ZQ=Z2

since alternate angles are equal

therefore line are parallel

Answer 2

Step-by-step explanation:

Here,

ZRPQ=ZPQR (given)

In ∆ PQR

ZRPQ+ZPQR+ZQRP=180

2ZRPQ+ZQRP= 180

ZQRP= 180-2ZRPQ (1)

now, In a straight line PSR

ZPRQ+ZQRT+ZTRS=180

we know that

Z1=Z2 (given)

so,

ZPRQ+2ZTRS=180

ZPRQ= 180-2ZTRS (2)

equating (1) and (2) we get

180-2ZRPQ=180-2ZTRS

2ZTRS=2ZRPQ

ZTRS=ZRPQ

Thus we know that z1 is corresponding angle of P

which proves that PQ is parallel to RT.