00:01
For this problem, we're going to need to complete a proof in order to prove that triangle a -c -m is congruent to triangle b -d -m.
00:11
So to start this proof, i've drawn my diagram, i've marked all the information i've been given, and if you're completing a two -column proof, like as normal for these kinds of problems, you're going to want to create your table and have your steps on one side and your reasons on the other.
00:26
In these kinds of proofs, we're always going to have our given is our very first step.
00:31
So step two is i want to use the fact, some of my given information.
00:37
And i actually need to put one more piece that i'm going to use just now.
00:40
I was also given that m is the midpoint of segment a, b.
00:49
So because m is the midpoint of a .b, it splits a .b into two congruent parts.
00:55
So for my second step, i can write that am is congruent to b .m.
01:03
And for my reason, i can write by definition of midpoint.
01:16
So i have that these triangles have one shared congruent side.
01:23
For my next step, i'm going to use the fact that angle one and angle two are congruent to each other.
01:30
So because angle one and angle two are congruent to each other, the sides opposite of these angles must also be congruent.
01:36
That is c .m and d .m.
01:40
Have to be congruent to each other.
01:42
So that would be step three...