Question

Given: ("CB" ) ∥ ("ED" ) ; ("CB" ) ≅ ("ED" )

Prove: CBF ≅ EDF using isometric (rigid) transformations.


Outline the necessary transformations to prove CBF ≅ EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements.

Answer 1

CB // ED and both of BD and CE are transversals

The point E will be the image of point C by rotation 180° around point F

And The point D will be the image of point B by rotation 180° around point F

Rotation is a kind of transformation

So, ΔEDF will be the image of ΔCBF

So, ΔCBF ≅ ΔEDF

Another way:

So, ∠B = ∠D Alternate angles are congruent

and ∠C = ∠E Alternate angles are congruent

So, ΔCBF and ΔEDF have the following

1) ∠C = ∠E ⇒⇒⇒ Alternate angles are congruent (proved)

2) CB ≅ ED ⇒⇒⇒ Given

2) ∠B = ∠D ⇒⇒⇒ Alternate angles are congruent (proved)

From 1, 2 and 3

So, ΔCBF ≅ ΔEDF By SAS postulate