Question

Given: segment AB || segment DE, C is the midpoint of segment DB.
Prove: ΔABC ≅ ΔEDC

Fill in the missing statement for the proof.

Answer 1

Hmmmm...... I'm not that great at math lol. Excuse my long thinking..

Answer 2

Hello @Shantelsurry and Welcome to QuestionCove :)

The first step towards a geometry problem like this is to try to draw a picture that represents the situation

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Angle
Hello @Shantelsurry and Welcome to QuestionCove :)

The first step towards a geometry problem like this is to try to draw a picture that represents the situation
\(\color{#0cbb34}{\text{End of Quote}}\)
Lol thanks for coming in, I was afraid I wasn't going to be able to help the person.

Answer 4

Here is a quick drawing that I think represents the information that we have been given

Answer 5

Yes

Answer 6

A) ∠B ≅ ∠E
B) ∠A ≅ ∠E
C) ∠A ≅ ∠D
D) ∠C ≅ ∠E

Answer 7

@Angle your drawing is a bit incorrect
It says `C is the midpoint of segment DB`, so the drawing should show that DC = CB

Answer 8

AHH Thanks for pointing that out @jimthompson5910

Answer 9

No problem

Answer 10

@Shantelsurry

First, why would the angle ACB and angle DCE be equal to each other?

Answer 11

It’s angle abc not acb

Answer 12

Why would the angles I just marked be equal to each other?

Answer 13

https://cdn.thinglink.me/api/image/567720530254233600/1240/10/scaletowidth

vertical angles are always going to be equal to each other

Answer 14

Now, in this problem we already know that we have a pair of Sides that are equal and a pair of Angles that are equal.

We would like another pair of Angles in order to use a rule such as AAS or ASA to prove triangle congruency

Answer 15

Statements Reasons
segment AB || segment DE given
C is the midpoint of DB given
segment DC ≅ segment BC definition of midpoint
∠B ≅ ∠D alternate interior angles of || lines are ≅
alternate interior angles of || lines are ≅
ΔABC ≅ ΔEDC AAS Theorem

Answer 16

ah I see

it is saying that you need another pair of Alternate Interior Angles

Answer 17

Yes

Answer 18

<B and <D are already used

what is another possible pair of angles that would be Alternate interior angles?

Answer 19

a and E

Answer 20

you got it