Proof of the theorem: Opposite sides of a parallelogram are congruent




Given the following parallelogram on the right, prove that opposite sides are congruent or equal.

Given: parallelogram ABCD

Prove: segment AB ≅ segment CD and segment BC ≅ AD

Since ABCD is a parallelogram, segment BC is parallel to segment AD according to the definition of a parallelogram.

By the same token, segment AB is parallel to segment DC according to the definition of a parallelogram.

Line AC is a transversal for segment BC and segment AD. This transversal creates alternate interior angles 1 and 4 which are equal as shown below.

By the same token, Line AC is a transversal for segment AB and segment DC. This transversal creates alternate interior angles 2 and 3 which are equal.

Moreover, segment AC ≅ segment AC by reflexive property.

Summary

∠1 ≅ ∠ 4

∠2 ≅ ∠ 3

segment AC ≅ segment AC

By ASA, triangle ABC ≅ triangle ADC

Therefore,segment AB ≅ segment CD and segment BC ≅ AD







Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz