Question

Line m is intersects sides AB and AC of triangle ABC in points P and Q respectively AP = 4.2 PB= 6.3 AQ= 4 QC = 6 state with reason whether line m is parallel to side BC or not

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In triangle ABC, AP=4.2cm, PB=6.3cm, AQ=4 cm, QC= cm}$

$\underline{\textsf{To find:}}$

$\textsf{Whether PQ is parallel to BC or not}$

$\underline{\textsf{Solution:}}$

$\mathsf{Converse\;basic\;propotionality\;theorem:}$

$\underline{\textsf{If a line divides two sides of a triangle in the same ratio,}}$

$\underline{\textsf{then the line is parallel to the third side}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{AP}{PB}=\dfrac{4.2}{6.3}}$

$\implies\mathsf{\dfrac{AP}{PB}=\dfrac{2}{3}}$......(1)

$\mathsf{\dfrac{AQ}{QB}=\dfrac{4}{6}}$

$\implies\mathsf{\dfrac{AQ}{QB}=\dfrac{2}{3}}$.......(2)

$\mathsf{From\;(1)\;and\;(2),\;we\;get}$

$\mathsf{\dfrac{AP}{PB}=\dfrac{AQ}{QB}}$

$\textsf{By converse of basic proportionality theorem}$

$\textsf{PQ is parallel to BC}$

$\textsf{Hence the line m is parallel to BC}$

Answer 2

Step-by-step explanation:

pq is parallel to bc....

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