MathematicsLet ABC be a triangle and D and E be two points on side AB such that AD = BC If DP || BC and EQ ||AC, prove PQ || AB.

Let ABC be a triangle and D and E be two points on side AB such that AD = BC If DP || BC and EQ ||AC, prove PQ || AB.

A
PQ || AD
B
PQ || BC
C
PQ || AC
D
PQ || AB

Solution:

Given that DP || BC and EQ || AC
AD  AP
So, DB PC
Again EQ || AC
BE  BQ
Therefore

EA QC

… (2)
Now AD = BE given AD + DE = BE + DE EA + BD
AD  BE  AC  BC
So DB EA DC QC
AD  BQ PC QC

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Type of relations_mathematics