write a two column proof

Question

Answer 1

Triangle JHM and JKM are congruent by SAS (they share side MJ, have equal right angles and MJ = JK as given by fact that they are bisected).

MH = MK by CPCTE (corresponding parts of congruent triangles are equal)

GH = GK because if a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment.

GM = GM by reflexive.

Triangle GKM and GHM are congruent by SSS.

<GKM and <GHM are congruent by CPCTE

Answer 2

Hi Buddy S.,

So what is your difficulty, is it that you do not feel certain what a 2-column proof format is, or do you need insight into the geometry and triangle congruency conditions?

If the latter, triangles JHM and JKM are congruent, by which condition? That gives you MH = MK. Then you use which condition to show congruency of the 2 given triangles? And then use definition of congruency for congruent angles.

If the former, you start with a given datum (column 1), reason (column 2) "stated". And work progressively as above, with reason for each step as the particular law of congruency, etc.

-- Cheers, -- Mr. d.