Question

Write the following proof. You can write this as a paragraph proof (don't forget to include your reasons!!) or as a two column proof. If you write it as a two column proof, you MUST number each statement and reason. (Hint: Prove ?ABC ? ?EDC first). Given: ?ABC and ?EDC, C is the midpoint of BD and AE Prove: AB || DE

          Write the following proof. You can write this as a paragraph proof (don't forget to include your reasons!!) or as a two column proof. If you write it as a two column proof, you MUST number each statement and reason. (Hint: Prove ?ABC ? ?EDC first).

Given: ?ABC and ?EDC, C is the midpoint of BD and AE
Prove: AB || DE

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Write the following proof. You can write this as a paragraph proof (don't forget to include your reasons!!) or as a two column proof. If you write it as a two column proof, you MUST number each statement and reason. (Hint: Prove ?ABC ? ?EDC first).

Given: ?ABC and ?EDC, C is the midpoint of BD and AE
Prove: AB || DE

Added by Thomas C.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Brent Burkett

12/16/2021

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We are given that triangle ABC and triangle EDC share a common vertex at C, and that C is the midpoint of both BD and AE. Show more…

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Write the following proof. You can write this as a paragraph proof (don't forget to include your reasons!!) or as a two column proof. If you write it as a two column proof, you MUST number each statement and reason. (Hint: Prove ┳ABC ≅ ┳EDC first). Given: ┳ABC and ┳EDC, C is the midpoint of BD and AE Prove: AB || DE

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Transcript

00:01 All right, so we have to do this proof.

00:02 We're given that c is the midpoint of a .e and bd, and we've got to prove that a, b, is parallel to d .e.

00:11 Okay, so we'll start by just kind of diagram and up our picture.

00:16 We have this triangle up here that i'm highlighting in red, and then we have this triangle down here that i'm highlighting in blue.

00:26 All right, so when we start with what we're given, that c is the midpoint.

00:34 So here's our statements.

00:36 I'm going to do two column proof.

00:42 And then here's our reasons over here to the right.

00:46 We draw a little better line there.

00:57 All right.

00:58 So start with what we're given.

01:00 C is the midpoint of these two line segments, a .e and pd.

01:16 That's given.

01:17 Now, since c is in the middle, so if you look at point c right here, it's in the middle of this line segment here.

01:30 So since it's in the middle, that means b, c, and c .d have to be congruent.

01:35 B .c.

01:37 Has to be congruent to c .d.

01:43 And then we could say the same thing since it's in the middle of a from a.

01:48 All the way to e since c's in the middle of those two points, then we can say ac is congruent to ce, and that's by the definition of the midpoint.

02:16 That's what it means to be in the middle.

02:18 It's equidistance from both ends of the line segment.

02:22 All right, so when we say those, when we get those, so now you can mark up our picture, this side right here, c .e, we just said, is congruent to ac, because of the definition of the midpoint.

02:39 We also know that b, c, this side here, is congruent to c .d.

02:49 So that's two sides.

02:51 So we can say these two triangles are now congruent, well, close...

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