homework 3 parallelogram proofs

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Question: Name: Unit 7: Polygons & Quadrilaterals Date: Homework 3: Parallelogram Proof This is a 2-page document! Directions: Complete each proof 1. Glven: ADACZARD 2CDB Prove: ABCD parallelogram Statements 1. AD IBC a LABD LCDB 3. AB II CD 4. ABCD is a Parallelogram 2. Given: WXYZ, WXZ E ZYZX Prove: WXYZ is a parallelogrom Statements Reasons 1.X YZ LwXZELYZX a. X2 #

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Parallelogram Proofs Worksheets

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.

Aligned Standard: High School Geometry - HSG-CO.C.11

• 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.
• Answer Keys - These are for all the unlocked materials above.

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.

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Calcworkshop

How To Prove a Parallelogram? 17 Step-by-Step Examples For Mastery!

// Last Updated: January 21, 2020 - Watch Video //

In today’s geometry lesson, you’re going to learn the 6 ways to prove a parallelogram.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

More specifically, how do we prove a quadrilateral is a parallelogram?

Finally, you’ll learn how to complete the associated 2 column-proofs.

Let’s jump in!

6 Properties of Parallelograms Defined

Well, we must show one of the six basic properties of parallelograms to be true!

• Both pairs of opposite sides are parallel
• Both pairs of opposite sides are congruent
• Both pairs of opposite angles are congruent
• Diagonals bisect each other
• One angle is supplementary to both consecutive angles (same-side interior)
• One pair of opposite sides are congruent AND parallel

So we’re going to put on our thinking caps, and use our detective skills, as we set out to prove (show) that a quadrilateral is a parallelogram.

This means we are looking for whether or not both pairs of opposite sides of a quadrilateral are congruent. Because if they are then the figure is a parallelogram.

In addition, we may determine that both pairs of opposite sides are parallel, and once again, we have shown the quadrilateral to be a parallelogram.

Opposite Sides Parallel and Congruent & Opposite Angles Congruent

Another approach might involve showing that the opposite angles of a quadrilateral are congruent or that the consecutive angles of a quadrilateral are supplementary. Both of these facts allow us to prove that the figure is indeed a parallelogram.

One Pair of Opposite Sides are Both Parallel and Congruent

Consecutive Angles in a Parallelogram are Supplementary

We might find that the information provided will indicate that the diagonals of the quadrilateral bisect each other. If so, then the figure is a parallelogram.

Diagonals of a Parallelogram Bisect Each Other

A tip from Math Bits says, if we can show that one set of opposite sides are both parallel and congruent, which in turn indicates that the polygon is a parallelogram, this will save time when working a proof.

In the video below:

• We will use the properties of parallelograms to determine if we have enough information to prove a given quadrilateral is a parallelogram.
• Find missing values of a given parallelogram.
• Write several two-column proofs (step-by-step).

Proving Parallelograms – Lesson & Examples (Video)

• Introduction to Proving Parallelograms
• 00:00:24 – How to prove a quadrilateral is a parallelogram? (Examples #1-6)
• Exclusive Content for Member’s Only
• 00:09:14 – Decide if you are given enough information to prove that the quadrilateral is a parallelogram. (Examples #7-13)
• 00:15:24 – Find the value of x in the parallelogram. (Examples #14-15)
• 00:18:36 – Complete the two-column proof. (Examples #16-17)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Last modified on August 3rd, 2023

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5 ways to prove a quadrilateral is a parallelogram.

This article will help us learn how to prove something is a parallelogram. More precisely, how to prove a quadrilateral is a parallelogram.

There are 5 basic ways to prove a quadrilateral is a parallelogram. They are as follows:

• Proving opposite sides are congruent
• Proving opposite sides are parallel
• Proving the quadrilateral’s diagonals bisect each other
• Proving opposite angles are congruent
• Proving consecutive angles are supplementary (adding to 180°)

Let us now prove the above statements one by one.

1) Proving Opposite Sides are Congruent

Prove that opposite sides of a parallelogram are congruent

To prove: AB ≅ CD, AD ≅ BC

Given: AB ∥ CD, AD ∥ BC

Draw in a diagonal AC

2) Proving Opposite Sides are Parallel

Prove that opposite sides of a parallelogram are parallel

To prove: AB ∥ CD, AD ∥ BC

Given: AB ≅ CD, AD ≅ BC

3) Proving Diagonals Bisect Each Other

Prove that the diagonals of a parallelogram bisect each other.

This is an “if and only if” proof, so there are two things to prove.

1. To prove: AE ≅ EC, BE ≅ ED

Given: ABCD is a parallelogram

And the converse

2. To prove: ABCD is a parallelogram

Given: AE ≅ EC, BE ≅ ED

4) Proving Opposite Angles are Congruent

Prove that the opposite angles of a parallelogram are congruent.

To prove: ∠ADC ≅ ∠ABC, ∠BAD ≅  ∠BCD

5) Proving Consecutive Angles are Supplementary

Prove that the consecutive angles of a parallelogram are supplementary (add up to 180°).

To prove: ∠ABC + ∠BCD = 180°

Extend BC till P

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