Home
Class 10
MATHS
In Delta ABC,D and E two points on AB su...

In `Delta ABC,D and E` two points on AB such that AD=BE. If `DP||BC and EQ||AC`, prove that such `PQ||AB`.

Text Solution

Verified by Experts

GIVEN `A Delta ABC and D,E ` are two points on AB such that `AB=BE`. Also, `DP||BC, and BC, and EQ|| AC`
TO PROOVE `PQ||AB`.
PROOF In `Delta ABC, DP||BC`.
`:. (AD)/(DB)=(AP)/(PC) " "...(i)` [ by Thale's theorme]
In `Delta CBA, EQ||AC`.
`:. (BE)/(EA)=(BQ)/(QC) " "` [ by Thale's theorme]
`rArr (AD)/(DB)=(BQ)/(QC) " "...(ii) [ :. BE=AD, EA=(ED+DA)=(DE+EB)=DB]`
From (i) and (ii), we get
`(AP)/(PC)=(BQ)/(QC)`
`:. PQ||AB` [ by the converse of Thale's theorem]
Promotional Banner

Similar Questions

Explore conceptually related problems

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.

In Delta ABC , D and E are two points on the sides AB and AC respectively so that DE || BC and (AD)/(BD) = (2)/(3) . Then ("the area of trapezium DECB")/("the area of " Delta ABC "equa to")

In Figure,AC>AB and D is the point on AC such that AB=AD. Prove that BC>CD

In Delta ABC, AB=AC and D is a point on side AC such that BD = BC, If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC ?

For a triangle ABC ,D and E are two points on AB and AC such that AD=(1)/(4)AB,AE=(1)/(4)AC . If BC = 12 cm, then DE is

In a Delta ABC, AB=AC=17cm D is a point on BC such that AD=15, CD=4 cm , find BD=?