Additive Property Of Equality Examples

To prove equality and congruence, we must use sound logic, backdrop, and definitions. Otherwise known as backdrop of equality.

Jenn (B.S., M.Ed.) of Calcworkshop® introducing properties of equality

Jenn, Founder Calcworkshop^®, fifteen+ Years Feel (Licensed & Certified Teacher)

Past knowing these logical rules, we will be able to manipulate, simplify, balance, and solve equations, every bit well every bit depict accurate conclusions supported past reasons.

The following backdrop allow united states to simplify, residuum, and solve equations.

Algebraic Properties Of Equality

1. Addition

Definition

If a = b, and then a + c = b + c

Example

If x – three = 7, and then x = 10 by adding three on both sides.

2. Subtraction

Definition

If a = b, so a – c = b – c

Example

If x + 2 = 11, and then x = 9 by subtracting 2 on both sides.

3. Multiplication

Definition

If a = b, then ac = bc

Instance

If x/four = 5, and so 10 = xx by multiplying by 4 on both sides.

4. Division

Definition

If a = b and c is not equal to 0, and so a / c = b / c

Example

If 8x = 16, then x = 2 by dividing by 8 on both sides.

5. Distributive

Definition

If a (b + c), and then a (b + c) = ab + ac

Case

If iii(ten + two), and so 3(10 + 2) = 3x + 6 past multiplying both x and ii past iii.

6. Exchange

Definition

If a = b, then either a or b may be substituted into any algebraic equation or expression for the other.

Instance

If 5x – 2y = z and x = y, then 5x – 2x = 12 or 5y – 2y = 12 by the substitution holding.

And these three properties define an equivalence relation, as accurately stated by Varsity Tutors.

properties of equality and congruence

Properties of Equality and Congruence

In the video below, yous'll larn to use these properties of equality, along with our previously learned definitions and postulates, to describe conclusions.

We'll beginning by showing you how to generate reasons for solving basic algebraic equations and then progress to supplying missing statements or reasons for equality and congruence involving geometric figures similar segments and angles.

All in all, we are discovering and learning how to use our final tool in our tool belt, thus enabling us to tackle ii-cavalcade proofs in the next lesson.

Properties of Equality – Lesson & Examples (Video)

38 min

Introduction to properties of equality and congruence
00:00:36 – Algebraic properties of equality and congruence (Examples #1-2)
Sectional Content for Member'south Only

00:13:26 – What are the missing reasons in the proof (Examples #ii-4)
00:19:52 – Fill up in the blanks to consummate the 2-column proof (Examples #5-7)
00:29:57 – Fill in the missing statements or reasons for the post-obit two-cavalcade proof (Examples #viii-9)
Practice Problems with Step-past-Step Solutions
Affiliate Tests with Video Solutions

Get access to all the courses and over 450 Hard disk drive videos with your subscription

Monthly and Yearly Plans Bachelor

Become My Subscription Now

Still wondering if CalcWorkshop is right for you lot?
Take a Bout and notice out how a membership can take the struggle out of learning math.

properties equality pinterest calcworkshop