if a transversal intersects two lines such that the bisectors of a pai

1.	if a transversal intersects two lines such that the bisectors of a pair of altemate interior angle are parallel, then prove that the two lines are parallel.
Answer» ong>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: Step-by-step explanation: PLEASE mark as brainliest answer

if a transversal intersects two lines such that the bisectors of a pair of altemate interior angle are parallel, then prove that the two lines are parallel.

Answer»

ong>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:

Step-by-step explanation:

PLEASE mark as brainliest answer