Question

Can you prove triangle BAC~ triangle DFE ? Justify your answer.

Answer 1

do u want to draw it or describe in formula?

Answer 2

You're given

AB || DF
AC || FE

Answer 3

The attachment is the drawing I just need to know if I can prove if the triangles are similar or not.

Answer 4

Yes wouldnt I need to have the other side also

Answer 5

Because you have two sets of parallel sides, the corresponding angles will be congruent.

Answer 6

AB~DF
AC~FE
=> BC~DE AND Angulars A> ~ F> so 2 triangels are similar

Answer 7

So I could prove this using AA? My answer would be yes because I am given two sets of parallel sides making their corresponding angles congruent?

Answer 8

@Hr.Tboy, that is not the proper way to start the proof. You don't start with statements that are not given.

Answer 9

They don't make me write proofs

Answer 10

You are given
AB || DF
AC || FE

However, you are not given that
AB ~ DF
AC ~ FE

Answer 11

ok that parallel is cause of 2 angulars D and B . u can put it instead of BC ~ DE in my first answer.

Answer 12

No No , there is no arguing on this one to! I just need to know if what I said would be a correct answer.

Answer 13

they are similar. it is final answer

Answer 14

And to justify my answer..... Because of the two sets of parallel sides I know that their corresponding angles are congruent letting me use the AA therm or postulate

Answer 15

they are similar cause of 2pair similar segments and 1pair angular. ok?

Answer 16

Angle Angle

Answer 17

D and B angles are congruent.

Answer 18

C and E angles are congruent too.

Answer 19

Okay thank you!

Answer 20

so we can also say cause of 2 congruent angels the 3th angels must be same. (sum of angels of 1triangle is 180).

Answer 21

ur welcome

Answer 22

@Hr.Tboy, as I stated earlier, you cannot begin with what is not given when proving.

Answer 23

@Hero ok finally i corrected it! is it wrong in ur opinion?

Answer 24

You begin by stating it is given that AB || DF and AC || FE. Next you say, Since AB || DF, ∠B ≅ ∠D. Since AC || FE, ∠C ≅ ∠E. Afterwards, you mention that since ∠B ≅ ∠D and ∠C ≅ ∠E, then by AA Similarity, ∠ABC ~∠DEF.