Question

6. 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 ZBPQ and
ZPQC respectively.
Prove that line AB | line CD.
Do Problem​

Answer 1

Answer:

ray PR ∥ SQ and PQ is transversal (given)

To find:

AB ∥ CD

∠ RPQ ≅ ∠ PQS (alternate angle) two angle formed when a line crosses two other lines, that lie on opposite side of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.)

X = y

∠ BPQ = 2x (ray PR bisect ∠ BPQ)

∠ PQC = 2y (ray SQ bisect ∠ PQC)

When a line, shape, or angle inti two exactly equal parts is called bisector.

X = y

2x = 2y (multiply 2 on both side)

∠ BPQ = ∠ PQC

But they form a pair of alternate angle that are congruent.

∴ AB ∥ CD (hence proved)

Step-by-step explanation:

$please \: mark \: me \: brilliance$

English :- follôw me for many type of answers

Hindi. :- कई तरह के जवाबों के लिए मुझे फॉलो करें

Gujarati :- ઘણા બધા જવાબો માટે મને ફોલો કરો