Question

Given segment AB is parallel to segment CD, angle B is ≅ angle D and segment BF ≅ segment ED. Prove triangle ABF ≅ triangle CED

o.o/ one moment i am drawing the diagram.

Answer 1

alright, don't there also need to be marks like this to show segment BF ≅ ED?

Answer 2

I left off a pair of congruent sides on my diagram so I added them.

Answer 3

oh okay o:now what can i do?

Answer 4

Looking at the parallel lines, find a pair of angles that you can show to be congruent. Look for a pair of angles that are also parts of the two triangles.

Answer 5

With regard to parallel lines cut by a transversal, what kind of angles are the angles marked in red in the triangles?

Answer 6

are angles A and C congruent?
are they reflexive angles?o.o

Answer 7

Angles A and C are alternate interior angles formed by two parallel lines cut by a transversal. So, angles A and C are congruent.

Now, we have enough to prove that the two triangles are congruent.

Answer 8

Given segment AB is parallel to segment CD, angle B is ≅ angle D and segment BF ≅ segment ED.

Prove triangle ABF ≅ triangle CED

1. angle B is ≅ angle D

2. segment BF ≅ segment ED

3. segment AB is parallel to segment CD

4. Angle A is congruent to Angle C

5. triangle ABF ≅ triangle CED

Okay, your task is to supply the reasons.

Answer 9

3. given?
4. alternate interior postulate?
5. CPCTC?

Answer 10

1. Given
2. Given
3. Given
4. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. (That may be the Alternate Interior Postulate in your book.)

5. No. You cannot use CPCTC unless you know that you have congruent triangles.

The question is: how do we know that the triangles are congruent?

Answer 11

It is one of these on the attachment, Proving Triangles Congruent.

Answer 12

@Kitteh

Answer 13

ummm could it be sas?

Answer 14

@Kitteh

Answer 15

yes i do seee it o:
so then do we have two angles and a side?x:

Answer 16

1. Given
2. Given
3. Given
4. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. (That may be the Alternate Interior Postulate in your book.)
5. AAS Theorem

Answer 17

Thank you so much :D