Question

a straight line drawn parallel to the side if bc of triangle abc meet ab and ac at points p and q respectively if ab=3ap find pq : bc​

Answer 1

Answer: 1/9

Step-by-step explanation: R.E.F image  

Given, AB=3AP...(1)

we can prove the two triangles  

are similar using  

1) AA (Angle-Angle)

2) SSS (side-side-side)

3) SAS (side-Angle-side)

In this case.

∠A is common to both the  

ΔABC and ΔAPQ

Also, ∠B≅∠P (corresponding angles)

∴ using AA theorem it is proved  

that ΔABC∼ΔAPQ

[Note :- Similarity sign is ∼]

Therm : The two similar Δs , the ratio of  

their area is the square of the

ratio of their sides.

Hence.

AreaofΔAPQ

AreaofΔABC

​  

=  

(AP)  

2

 

(AB)  

2

 

​  

 

=(  

AP

AB

​  

)  

2

 

from (1)

AreaofΔABC

AreaofΔAPQ

​  

=(  

AB

AP

​  

)  

2

=(  

3

1

​  

)  

2

 

=  

9

1

Answer 2

Answer:

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Step-by-step explanation:

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