Properties Of Equality And Congruence

To prove equality and congruence, we must use audio logic, backdrop, and definitions. Otherwise known equally properties of equality.

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

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

By knowing these logical rules, nosotros will be able to manipulate, simplify, balance, and solve equations, likewise as draw accurate conclusions supported past reasons.

The following properties let us to simplify, residuum, and solve equations.

Algebraic Backdrop Of Equality

1. Improver

Definition

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

Example

If x – 3 = 7, so x = 10 by adding three on both sides.

2. Subtraction

Definition

If a = b, then a – c = b – c

Example

If ten + two = 11, so x = ix by subtracting ii on both sides.

3. Multiplication

Definition

If a = b, then ac = bc

Case

If 10/4 = five, then ten = 20 by multiplying by four on both sides.

iv. Sectionalisation

Definition

If a = b and c is non equal to 0, so a / c = b / c

Example

If 8x = 16, then 10 = two by dividing past 8 on both sides.

5. Distributive

Definition

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

Example

If 3(x + 2), then 3(x + ii) = 3x + 6 by multiplying both x and 2 by three.

6. Substitution

Definition

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

Example

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

And these three backdrop define an equivalence relation, as accurately stated past Varsity Tutors.

properties of equality and congruence

Properties of Equality and Congruence

In the video below, you'll learn to apply these properties of equality, along with our previously learned definitions and postulates, to draw conclusions.

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

All in all, we are discovering and learning how to apply our final tool in our tool belt, thus enabling u.s. to tackle two-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-ii)
Sectional Content for Member'south Merely

00:13:26 – What are the missing reasons in the proof (Examples #2-4)
00:xix:52 – Make full in the blanks to complete the two-column proof (Examples #five-7)
00:29:57 – Fill in the missing statements or reasons for the following 2-column proof (Examples #8-9)
Practise Problems with Step-by-Step Solutions
Affiliate Tests with Video Solutions

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