Question

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel. Please send the answer as soon as possible

Answer 1

Let AB ║ CD and EF be the transversal passing through the two parallel lines at P and Q respectively. PR and QS are the bisectors of ∠EPB and ∠PQD.
 Since the corresponding angles of parallrl lines are equal,
∴∠EPB = ∠PQD
∴1/2 ∠EPB = 1/2 ∠PQD
∴∠EPR = ∠PQS
 But they are corresponding angles of PR and QS
Since the corresponding angles are equal
∴ PR ║ QS

Answer 2

Answer:

ANSWER

The transversal AD intersects the two lines PQ and RS at points B and C respectively. BE is the bisector of ∠ABQ and CF is the bisector of ∠BCS.

As, BE is the bisector of ∠ABQ, then,

∠ABE=21∠ABQ

In the same way,

∠BCF=21∠BCS

Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,

∠ABE=∠BCF

21∠ABQ=21∠BCS

∠ABQ=∠BCS

Therefore, by the converse of corresponding angle axiom,

PQ∥RS.

Step-by-step explanation:

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