Let abc be a triangle and d and e be two points on side ab such that ad= be . If dp||BC and eq|| AC , then prove that pq || ab . .............
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Given
In triangle ABC D and E are two points on AB and DP is parallel to BC and EQ is parallel to AC
To prove
PQ parallel to AB
In triangle ABC D and E are two points on AB and DP is parallel to BC and EQ is parallel to AC
To prove
PQ parallel to AB
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Kanikashah:
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Answered by
159
Heya friend,
Here is your answer,
Given: ABC is a triangle such that AD = BE Also DP ll BC and EQ ll AC
Prove that: PQ ll AB
Proof:
In the triangles ADP and EBQ;
=> AD = BE (given)
=> Angle(DAP) = Angle(BEQ)
[corresponding interior angles]
=> Angle(ADP) = Angle(EBQ)
[corresponding interior angles]
Therefore,
By, ASA congruency triangle triangle(ADP) is congruent to triangle(EBQ).
Thus,
=> By CPCT: PD = BQ ..........(1)
=> And PD ll BQ [given] ..........(2)
Now,
Since one pair of opposite side are equal and parallel.
Therefore, the quadrilateral DPQB is a parallelogram and PQ || DB. (hence proved)
Hope it helps you,
Thank you.
Here is your answer,
Given: ABC is a triangle such that AD = BE Also DP ll BC and EQ ll AC
Prove that: PQ ll AB
Proof:
In the triangles ADP and EBQ;
=> AD = BE (given)
=> Angle(DAP) = Angle(BEQ)
[corresponding interior angles]
=> Angle(ADP) = Angle(EBQ)
[corresponding interior angles]
Therefore,
By, ASA congruency triangle triangle(ADP) is congruent to triangle(EBQ).
Thus,
=> By CPCT: PD = BQ ..........(1)
=> And PD ll BQ [given] ..........(2)
Now,
Since one pair of opposite side are equal and parallel.
Therefore, the quadrilateral DPQB is a parallelogram and PQ || DB. (hence proved)
Hope it helps you,
Thank you.
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