Question

A transversal EF of line AB and line CD intersect the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisector of

Answer 1

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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)

Hope it helps you ❣️☑️☑️☑️