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How to Prove Opposite Sides of a Parallelogram are Equal

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Trinity ☕️

9/21/2023

Geometry

FILLED Quadrilateral/Parallelogram Proof Practice + Notes

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Geometry

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Congruence

/

Theorems Concerning Quadrilateral Properties

How to Prove Opposite Sides of a Parallelogram are Equal

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

156

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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Subjects

Geometry

Congruence

Theorems Concerning Quadrilateral Properties

 

Geometry

•

156

•

Sep 21, 2023

•

2 pages

How to Prove Opposite Sides of a Parallelogram are Equal

user profile picture

Trinity ☕️

@coffee_breakk

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... Show more

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"

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

Sign up to see the contentIt'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.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

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Greenlight Bonnie

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Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

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