2 Column Proof (Parallelogram)

Apples+Pears^2

New member
Joined
Feb 16, 2021
Messages
5
Screenshot 2021-02-19 at 1.58.43 PM.png
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:
StatementsReasons
ABDF is a parallelogramgiven
DB parallel to FA, DF parallel to BAdefinition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAFOpposite angles congruent
Thanks!
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
10,590
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:
StatementsReasons
ABDF is a parallelogramgiven
DB parallel to FA, DF parallel to BAdefinition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAFOpposite 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

New member
Joined
Feb 16, 2021
Messages
5
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:
StatementsReasons
ABDF is a parallelogramgiven
DB parallel to FA, DF parallel to BAdefinition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAFOpposite angles congruent
DF parallel to BA. BA line with BC. DF parallel ACTransitive property of =
Angle EDF = Angle DCBCorresponding angles
Angle CDB = Angle DEFCorresponding angles
Triangle CBD ~ Triangle DFEAA similarity (steps 5, 6)
I think this is correct. If there's anything missing or incorrect, let me know! :D
Thank you!
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
10,590
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:
StatementsReasons
ABDF is a parallelogramgiven
DB parallel to FA, DF parallel to BAdefinition of parallelogram
Angle DBF = Angle DFA, Angle BDF = Angle BAFOpposite angles congruent
DF parallel to BA. BA line with BC. DF parallel ACTransitive property of =
Angle EDF = Angle DCBCorresponding angles
Angle CDB = Angle DEFCorresponding angles
Triangle CBD ~ Triangle DFEAA similarity (steps 5, 6)
I think this is correct. If there's anything missing or incorrect, let me know! :D
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.
 
Top