Question

PLEASE HELP:)

A line segment BK is an angle bisector of ΔABC. A line KM intersects side BC such, that
BM = MK. m∠MBK≅m∠_____ by reason_______

Answer 1

<mkb 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.
Hope this helps!

Answer 2

Explanation:

Given that a line segment BK is an angle bisector of triangle ABC.

When the line KM intersects BC such that BM=MK

we find an isosceles triangle BMK with two sides equal

Hence by isosceles triangles theorem, two angles opposite equal sides would be equal

i.e.
`m∠MBK≅m∠_BKM____`

The isosceles triangle theorem states that If two sides of a triangle are congruent, then angles opposite those sides are congruent.