2 Column Proof (Parallelogram)

[Apples+Pears^2]

Hello! I have to write a 2 column proof.
Given: ABDF is a parallelogram.
Prove: Triangle CBD is similar to Triangle DEF.

All I have so far is the black annotated markings on parallelogram ABDF, which is what I know of parallelograms. I don't know how to prove them similar yet. And all I have so far for the proof:

Statements	Reasons
ABDF is a parallelogram	given
DB parallel to FA, DF parallel to BA	definition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAF	Opposite angles congruent

Thanks!

 

[Dr.Peterson]

View attachment 25208
Hello! I have to write a 2 column proof.
Given: ABDF is a parallelogram.
Prove: Triangle CBD is similar to Triangle DEF.

All I have so far is the black annotated markings on parallelogram ABDF, which is what I know of parallelograms. I don't know how to prove them similar yet. And all I have so far for the proof:

Statements	Reasons
ABDF is a parallelogram	given
DB parallel to FA, DF parallel to BA	definition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAF	Opposite angles congruent

Thanks!

Good start; that's what the givens imply.

Now go to the goal: what would it take to prove the triangles similar?

Then connect the two: does anything you already know imply anything you need to know?

If you run out of ideas, look for things that are implied by what the givens imply -- for example, are there other angles that are congruent because of the parallel lines?

 

[Apples+Pears^2]

Good start; that's what the givens imply.

Now go to the goal: what would it take to prove the triangles similar?

Then connect the two: does anything you already know imply anything you need to know?

If you run out of ideas, look for things that are implied by what the givens imply -- for example, are there other angles that are congruent because of the parallel lines?

I guess you would use AA similarity? So I would need to prove that 2 angles of one triangle are congruent to 2 angles of the other triangle. Oh that makes sense
Here's what I have of the proof now:

Statements	Reasons
ABDF is a parallelogram	given
DB parallel to FA, DF parallel to BA	definition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAF	Opposite angles congruent
DF parallel to BA. BA line with BC. DF parallel AC	Transitive property of =
Angle EDF = Angle DCB	Corresponding angles
Angle CDB = Angle DEF	Corresponding angles
Triangle CBD ~ Triangle DFE	AA similarity (steps 5, 6)

I think this is correct. If there's anything missing or incorrect, let me know!
Thank you!

 

[Dr.Peterson]

I guess you would use AA similarity? So I would need to prove that 2 angles of one triangle are congruent to 2 angles of the other triangle. Oh that makes sense
Here's what I have of the proof now:

Statements	Reasons
ABDF is a parallelogram	given
DB parallel to FA, DF parallel to BA	definition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAF	Opposite angles congruent
DF parallel to BA. BA line with BC. DF parallel AC	Transitive property of =
Angle EDF = Angle DCB	Corresponding angles
Angle CDB = Angle DEF	Corresponding angles
Triangle CBD ~ Triangle DFE	AA similarity (steps 5, 6)

I think this is correct. If there's anything missing or incorrect, let me know!
Thank you!

You've got the idea. Did you mention DB || EA? There may be a couple little details like that, which depend on style.