6.3 Proving Quadrilaterals are Parallelograms

In this section, we learned how to prove quadrilaterals are parallelograms.

Here are some problems you might find from this section and how to do them.

Firstly, you might be asked to write a proof to prove a quadrilateral is a parallelogram.

Example 1



Given: Angle D is supplementary to angle A and angle C
Prove ABCD is a parallelogram.

Statements

1) Angle D is supplementary to angle A and angle C
2) Line AB is parallel to line DC
3) Line AD is parallel to line BC
4) ABCD is a parallelogram

Reasons
1) Given
2) Consecutive Interior Angles Converse
3) Consecutive Interior Angles Converse
4) Definition of a parallelogram

Example 2

You might be asked to decide if there's enough information to prove a quadrilateral is a parallelogram.


If opposite sides of a quadrilateral are congruent, then it's a parallelogram.


Here are some problems to try on your own.

Are you given enough info to decide if the quadrilateral is a parallelogram?

1)


2)


3)

4)

Given: Angle E is congruent to angle G
Angle F is congruent to angle H
Prove: EFGH is a parallelogram


Directions: Use the definition or theorem to prove that HIJK is a parallelogram.
H(-1,6), I(3,5), J(5, -3), K(1,-2).

5) Definition of a parallelogram