## Parallelogram Proofs

#### Aligned To Common Core Standard:

**High School Congruence** - HSG-CO.C.11

How to Prove Theorems of Parallelograms?
Definition: A parallelogram is a quadrilateral that has both pairs of opposite sides parallel.
**Sides** - Theorem 1: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram.
**Angles** - Theorem 2: If a quadrilateral has 2 sets of opposite angle which are also congruent, then it is a parallelogram
Theorem 3: If a quadrilateral has consecutive angles that are also supplementary, then it is a parallelogram.
**Diagonals** - Theorem 4: If a quadrilateral has diagonals that bisect each other, it is a parallelogram.
**Combo** - Theorem 5: If a quadrilateral has one of the opposite sides, which are both parallel and congruent, then it is a parallelogram.
P.S. This method is easier compared to others as it requires less time and energy. This series of lessons and worksheets focuses on using various theorems related to parallelogram proofs.

### Printable Worksheets And Lessons

- Proofs for Opposites
Step-by-step Lesson - Hopefully you know what opposite angles
are for this one.

- Guided Lesson
- Complementary angles and the known properties of parallelograms
are used to solve these.

- Guided Lesson
Explanation - These proofs are more matter of fact than step
by step like the others on the site.

- Practice Worksheet
- You might need to review what the marking on the quadrilaterals
indicate to help them solve these.

- Matching Worksheet
- I like these questions because they force you to think in a themed
manner.

#### Homework Sheets

We really cover the hidden geometry of quadrilaterals here.

- Homework 1 - A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
- Homework 2 - If a quadrilateral is a parallelogram, then opposite angles are equal in measure.
- Homework 3 - If 2 parallel lines are cut by a transversal, then corresponding angles are equal in measure.

#### Practice Worksheets

Here is where geometry and algebra start to collide and form into something abstract.

- Practice 1 - Based on the shape, are the opposite sides are parallel?
- Practice 2 - What is the length of side BC and side CD in parallelogram ABCD?
- Practice 3 - If DEFG is a parallelogram. Find the value of x?

#### Math Skill Quizzes

This is where geometry starts to get a little bit tougher.

- Quiz 1 - You will given a number of situations that you need to explain. Are angle C and A supplementary angles?
- Quiz 2 - Find if both pairs of opposite sides are parallel in this parallelogram?
- Quiz 3 - When you are given a single angle, what are all the other angles? Find the value of angle Q.

### Why Are These Types of Proofs Important?

The purpose of proving that a geometric shape is in fact the shape that it appears to be is that it leads us to complete understand the geometry behind the shape in question. It also tells us that all the properties that are specific to shape apply to our situation. In the case of a parallelogram, if we can identify or prove that is the shape of a figure it allows us to immediate know six things about this shape. We would intuitively know that the opposite sides and angles are equivalent. Any consecutive angles in the figure are supplementary. The diagonals are bisectors of each other, and they can easily be separated into two congruent triangles by simply drawing a line. While all these facts are nice and neat, you probably still do not see the purpose of it all? In the real world when a building, home, or structure are being created having this information is critical. If we can prove that a room possesses this shape, we can easily determine where to position our materials to make them level and straight. This particular shape comes up in your more modern new wave construction. Most home dwelling still stick to the standard rectangle and square rooms. You will see this geometric shape used in parking lots to maximum the number of spaces for vehicles while at the same time developing a flow of traffic. You will find this pretty common at most shopping malls.