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A line segment BK is an angle bisector of ΔABC. A line KM intersects side BC such, that BM = MK. Prove: KM ∥ AB .

m∠MBK≅m∠______, by reason_________

Respuesta :

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Answer:

<MBK because of the isosceles triangle theorem. If two sides of a triangle are congruent, it is isosceles, so the angles opposite them are also congruent.

Step-by-step explanation:

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Answer:

<MBK is approximately equals to < MKB, by reason of property of an isosceles triangle.

Step-by-step explanation:

In the given triangle, < ABC has a bisector K which divides the angle into two equal parts. Then given that BM = MK,

                < BMK + < CMK = [tex]180^{0}[/tex] (sum of angles on a straight line)

                < ABC = < CMK (corresponding angles)

Thus, KM ll AB.

Considering the isosceles triangle KBM,

                BM = MK  (given property of the triangle)

Since two sides are equal, then two angles would be equal.

So that,

                <MBK = < MKB (the opposite angles of the sides of an isosceles triangle are equal)