P and Q are respectively points on the Ab and AC of Triangle ABC.If AP=2cm,PB=4cm,AQ=3cm and QC=6cm,prove that BC=3PQ.

Please answer fast I have a test tommorow.

Question

P and Q are respectively points on the Ab and AC of Triangle ABC
If AP=2cm,PB=4cm,AQ=3cm and QC=6cm,prove that BC=3PQ
Please answer fast I have a test tommorow

Gursheen kaur. · Accepted Answer

Given: AP = 2 cm, PB = 4 cm , AQ = 3 cm and QC = 6 cm

AB = AP + PB = 2+4=6 cm

AC = AQ + QC = 3+6=9 cm

in the triangles APQ and ABC,

$\frac{A P}{A B} = \frac{2}{6} = \frac{1}{3} \frac{A Q}{A C} = \frac{3}{9} = \frac{1}{3} \Rightarrow \frac{A P}{A B} = \frac{A Q}{A C}$

and $∠ P A Q = ∠ B A C$

the ratio of the two corresponding sides are equal and angle contained by these two sides are equal.

therefore $Δ A P Q \approx Δ A B C$

by the similarity rule:

$\frac{P Q}{B C} = \frac{A P}{A B} = \frac{1}{3} \Rightarrow \frac{P Q}{B C} = \frac{1}{3} \Rightarrow B C = 3 P Q$

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P and Q are respectively points on the Ab and AC of Triangle ABC.If AP=2cm,PB=4cm,AQ=3cm and QC=6cm,prove that BC=3PQ. Please answer fast I have a test tommorow.

P and Q are respectively points on the Ab and AC of Triangle ABC.If AP=2cm,PB=4cm,AQ=3cm and QC=6cm,prove that BC=3PQ.

Please answer fast I have a test tommorow.