Given: EFGH is a ( square ). [ overlinemathrmAE cong...

Transcript

00:02 Okay, we're given that ef, g, h is a parallelogram.

00:06 We're given that a, e, b, f, c, g, and d are all congruent.

00:13 And we've got to prove the larger figure a, b, c, d is a parallelogram.

00:19 So i think my strategy will be to prove congruent triangles.

00:24 So i could show aed is congruent to c -g -b, and that a -f -b is congruent to c -d.

00:35 So the top and bottom, i think i can show those are congruent, left and right.

00:40 I think i can show are congruent.

00:42 And then we'll have opposite sides are congruent, therefore it's a parallelogram.

00:55 Okay, so let's get started.

00:56 So first off, since that central figure is a parallelogram, i know the opposite sides are, well, i know they're parallel, well.

01:12 But i think the best use would be to say they're congruent.

01:17 So these are congruent and then these are congruent.

01:21 Then we got all those given congruent measures.

01:26 You know what? i'll use three hash marks for this one.

01:29 So that way these i can all do one hash mark.

01:35 Did i do that right? a .e.

01:38 B, f, c, g, and d .h.

01:40 Yep.

01:43 Okay.

01:44 So if you look at the top triangle and the bottom triangle, triangle.

01:47 I see e, d would be congruent to g b by the angle addition, a segment addition postulate.

01:55 They've got, they're formed by two congruent, two sets of congruent segments.

02:01 Then i see a .e is congruent to c .g.

02:06 So i've got those two sides.

02:09 I just need to find, find an angle.

02:13 Well, one thing i know about parallelograms is that the opposite angles would be congruent...

Given: EFGH is a ( square ). [ overline{mathrm{AE}} cong overline{mathrm{BF}} cong overline{mathrm{CG}} cong overline{mathrm{DH}} ] Prove: ( A B C D ) is a ( square ).