Question

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

Answer 1

See explanation

Explanation:

1. BK is an angle B bisector, then

`\angle ABK\cong \angle CBK` (definition of angle bisector)

2. BM = MK, then

triangle BMK is isosceles triangle with base BK.

3. Angles adjacent to the base of isosceles triangle are congruent, then

`\angle MBK \cong \angle BKM`

Note that angle MBK is the same as angle CBK.

4. By substitution property,

`\angle ABK \cong \angle BKM`

5. By alternate interior angles theorem,

if
`\angle ABK \cong \angle BKM`, then
`AB\parallel KM`