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How to Prove Opposite Sides of a Parallelogram are Equal

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How to Prove Opposite Sides of a Parallelogram are Equal
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Trinity ☕️

@coffee_breakk

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Verified Study Note

A comprehensive guide to parallelogram proofs practice, focusing on proving geometric properties including opposite sides of parallelogram congruent and how diagonals bisect each other in parallelogram.

  • The guide covers essential parallelogram properties including opposite sides, angles, and diagonal relationships
  • Detailed proofs are presented using statements and reasons format, incorporating geometric theorems like ASA and CPCTC
  • Multiple examples demonstrate how to prove opposite angles are equal and diagonals bisect each other
  • Key concepts include alternate interior angles, reflexive properties, and parallel line relationships
  • Practice problems reinforce understanding of parallelogram properties and proof techniques

9/21/2023

103

11 - parallel
Quadrilateral
Square
Rectangle
Parallelogram
Rhombus
Kite
Image
1-perpendicular
Sides
all equal
opposite side ll
adjacent are.

View

Page 2: Advanced Parallelogram Proofs

This page delves into more complex proofs involving opposite angles and diagonal properties of parallelograms. Multiple proof exercises demonstrate different approaches to proving parallelogram properties.

Highlight: The page presents three distinct proofs:

  1. Proving opposite angles are congruent
  2. Proving diagonals bisect each other
  3. Proving all pairs of opposite angles are equal

Example: To prove diagonals bisect each other in parallelogram JKLM:

  1. Begin with parallel sides property
  2. Use alternate exterior angles
  3. Apply triangle congruence theorems
  4. Conclude that JN=NL and KN=MN

Quote: "Using diagonal AC we could follow a similar argument to prove that ∠B = ∠D"

11 - parallel
Quadrilateral
Square
Rectangle
Parallelogram
Rhombus
Kite
Image
1-perpendicular
Sides
all equal
opposite side ll
adjacent are.

View

Page 1: Fundamental Parallelogram Properties and Proofs

This page introduces the fundamental properties of parallelograms and presents a detailed proof showing that opposite sides are congruent. The content systematically builds from basic definitions to complex proofs.

Definition: A parallelogram is a quadrilateral with two pairs of parallel sides.

Highlight: Key properties of parallelograms include parallel opposite sides, congruent opposite angles, and bisecting diagonals.

Example: The proof that opposite sides of a parallelogram are congruent uses the following steps:

  1. Start with parallelogram ABCD
  2. Draw diagonal DB
  3. Use alternate interior angles
  4. Apply ASA triangle congruence
  5. Conclude with CPCTC

Vocabulary: CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.

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How to Prove Opposite Sides of a Parallelogram are Equal

user profile picture

Trinity ☕️

@coffee_breakk

·

6 Followers

Follow

Verified Study Note

A comprehensive guide to parallelogram proofs practice, focusing on proving geometric properties including opposite sides of parallelogram congruent and how diagonals bisect each other in parallelogram.

  • The guide covers essential parallelogram properties including opposite sides, angles, and diagonal relationships
  • Detailed proofs are presented using statements and reasons format, incorporating geometric theorems like ASA and CPCTC
  • Multiple examples demonstrate how to prove opposite angles are equal and diagonals bisect each other
  • Key concepts include alternate interior angles, reflexive properties, and parallel line relationships
  • Practice problems reinforce understanding of parallelogram properties and proof techniques

9/21/2023

103

 

10th

 

Geometry

2

11 - parallel
Quadrilateral
Square
Rectangle
Parallelogram
Rhombus
Kite
Image
1-perpendicular
Sides
all equal
opposite side ll
adjacent are.

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Page 2: Advanced Parallelogram Proofs

This page delves into more complex proofs involving opposite angles and diagonal properties of parallelograms. Multiple proof exercises demonstrate different approaches to proving parallelogram properties.

Highlight: The page presents three distinct proofs:

  1. Proving opposite angles are congruent
  2. Proving diagonals bisect each other
  3. Proving all pairs of opposite angles are equal

Example: To prove diagonals bisect each other in parallelogram JKLM:

  1. Begin with parallel sides property
  2. Use alternate exterior angles
  3. Apply triangle congruence theorems
  4. Conclude that JN=NL and KN=MN

Quote: "Using diagonal AC we could follow a similar argument to prove that ∠B = ∠D"

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App

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11 - parallel
Quadrilateral
Square
Rectangle
Parallelogram
Rhombus
Kite
Image
1-perpendicular
Sides
all equal
opposite side ll
adjacent are.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Fundamental Parallelogram Properties and Proofs

This page introduces the fundamental properties of parallelograms and presents a detailed proof showing that opposite sides are congruent. The content systematically builds from basic definitions to complex proofs.

Definition: A parallelogram is a quadrilateral with two pairs of parallel sides.

Highlight: Key properties of parallelograms include parallel opposite sides, congruent opposite angles, and bisecting diagonals.

Example: The proof that opposite sides of a parallelogram are congruent uses the following steps:

  1. Start with parallelogram ABCD
  2. Draw diagonal DB
  3. Use alternate interior angles
  4. Apply ASA triangle congruence
  5. Conclude with CPCTC

Vocabulary: CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.

Sign up for free!

Learn faster and better with thousand of available study notes

App

By signing up you accept Terms of Service and Privacy Policy

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying