If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that two lines are parallel
Answers
Step-by-step explanation:
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.
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,
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
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∠ABQIn the same way,
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∠ABQIn the same way,∠BCF=21∠BCS
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,∠ABE=∠BCF
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,∠ABE=∠BCF21∠ABQ=21∠BCS
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,∠ABE=∠BCF21∠ABQ=21∠BCS∠ABQ=∠BCS
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,∠ABE=∠BCF21∠ABQ=21∠BCS∠ABQ=∠BCSTherefore, by the converse of corresponding angle axiom,
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∠ABQIn the same way,∠BCF=21∠BCSSince BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,∠ABE=∠BCF21∠ABQ=21∠BCS∠ABQ=∠BCSTherefore, by the converse of corresponding angle axiom,PQ∥RS.
