Notice that both polygons have a side in common. Use the Alternate Interior Angles Theorem to establish a relation between the angles formed at B and the angles formed at E.
See solution.
Practice makes perfect
Let's begin by pointing out the congruent sides of the two polygons.
Due to the Reflexive Property of Congruent Segments, we have EB≅ BE. This means that both polygons above have all its corresponding sides congruent. Next, let's highlight the corresponding congruent angles.
Notice that AC ∥ DF and BE is a transversal. Then, by the Alternate Interior Angles Theorem we have that ∠ ABE ≅ ∠ FEB and ∠ BED ≅ ∠ EBC.
Since both polygons have all its corresponding parts congruent, they are congruent by definition.
Angles
Sides
∠ A ≅ ∠ F
BA ≅ EF
∠ABE ≅ ∠FEB
AD ≅ FC
∠BED ≅ ∠EBC
DE ≅ CB
∠ D ≅ ∠ C
EB≅ BE
We are now ready to make a paragraph proof.
Completed Proof
From the given diagram, we have that BA ≅ EF, AD ≅ FC, and DE ≅ CB. Notice that BE is a common side for both polygons, and due to the Reflexive Property of Congruent Segments, we have EB≅ BE.
The 4 pairs of corresponding sides
of the two polygons are congruent
Additionally, we can see that ∠ A≅ ∠ F and ∠ D ≅ ∠ C. Note that the sides AC and DF are parallel and BE is a transversal. So, by using the Alternate Interior Angles Theorem we have that ∠ ABE ≅ ∠ FEB and ∠ BED ≅ ∠ EBC.
The 4 pairs of corresponding angles
of the two polygons are congruent
Consequently, both polygons have corresponding parts congruent, which implies they are congruent.
