Question

1. Write a two-column proof for the following conjecture. Given: K is the midpoint of . Prove: is an isosceles triangle.

Answer 1

1. Angle LKM and Angle JKM are supplementary 1. LJ is a straight line, since K is a midpoint
2. LK = KJ 2. K is a midpoint
3. Angle L + Angle M + Angle LKM = Angle LKM + Angle MJK 3. A triangle's total degrees is equal to the total degrees of two supplementary angles.
4. Angle JKM = Angle L + Angle M 4. Simple Algebra: Subtract Angle 
5. LK = KM 5. MK is intersecting LJ at a midpoint.
6. Triangle LKM is isoceles 6. Two of three sides and angles are equal.