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In triangle ABC, points P and Q lie on the side BC. It is given that BP = 1, PQ = 3, and QC = 1. The line passing through P and parallel to AB intersects AB in K and the line passing through Q and parallel to AB intersects AC in L. Show that KL || BC by proving that triangles AKL and ABC are similar. 

 

Find another way to prove that KL || BC, by showing that a certain quadrilateral in the diagram is a parallelogram.

 

Include a diagram (optional)

 Aug 4, 2021
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Let me correct the question first (red ink).

 

In a triangle, ABC, points P and Q lie on the side BC. It is given that BP = 1, PQ = 3, and QC = 1. The line passing through P and parallel to AC intersects AB in K and the line passing through Q and parallel to AB intersects AC in L. Show that KL || BC by proving that triangles AKL and ABC are similar. 

Find another way to prove that KL || BC, by showing that a certain quadrilateral in the diagram is a parallelogram.

 

Hint:    ∠A = 90º         AB = 3        AC = 4

 

Now you can solve it. smiley

 Aug 4, 2021

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