30. PLis the angle bisector of KPM.Which can you conclude from this statement? You also can see this question number 30 on this website.Please add hyperlink.

Question

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How answer is A and i want to learn how to find a length of KL. Please help.

Answer 1

Because PL bisects ∡KPM,
∡LPJ ≅ ∡LPN
Since both are right triangles, and they share hypotenuse LL, ∆ LPJ ≅ ∆ LPN by ASA. So, LJ ≅ LN
Using similar reasoning, using SAS, ∆LJK ≅ ∆LNM.
So, LN ≅ LJ

Answer 2

oops. typo. they share hypotenuse PL