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)

Guest Aug 4, 2021

#1**0 **

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.

Guest Aug 4, 2021