Question

In a triangle XYZ, LM || YZ and bisectors YN and ZN of angle Y & angle Z respectively meet at N in LM.then YL+ZM=​

Answer 1

Step-by-step explanation:

One item of information that you neglected to mention, but I believe is the case, is that L lies on XY and M lies on XZ. If that's NOT the case, the problem cannot be answered. :-) So assuming it's true...

<LNY = <NYZ <------------------ Alternate interior angles are congruent.

<NYZ = 1/2 <Y <----------------- YN is the angular bisector of Y.

<LNY = 1/2 <Y <----------------- Substitution.

<LYN = 1/2 <Y <----------------- YN is the angular bisector of Y.

<LYN = <LNY <------------------ Substitution

Triangle LNY is isoceles <---- Congruent base angles.

LY = LN <--------------------------- Property of isoceles triangle.

A similar proof can be given to show that MZ = MN.

So... YL + ZM = LN + MN = LM