Download presentation

1
**2.5 Reasoning in Algebra and Geometry**

Algebraic properties of equality are used in Geometry. Will help you solve problems and justify each step. In Geometry, you accept postulates and properties as true. Some of the properties you accept as true are the properties of equality from Algebra.

2
**Properties of Equality**

Let a, b, and c be any real numbers. Addition Property: If a = b, then a + c = b + c. Subtraction Property: If a = b, then a - c = b - c. Multiplication Property: If a = b, then a * c = b * c. Division Property: If a = b and c ≠ 0, then a/c = b/c. Reflexive Property: a = a. Symmetric Property: If a = b, then b = a. Transitive Property: If a = b and b = c, then a = c. Substitution Property: If a = b, then b can replace a in any expression.

3
**Distributive Property**

Use multiplication to distribute a to each term of the sum or difference within the parentheses. Sum: a (b + c) = ab + ac Difference: a (b – c) = ab – ac

4
**Justifying Steps when Solving an Equation**

What is the value of x? Justify each step.

5
**Justifying Steps when Solving an Equation**

angles that form a linear pair are suppl. def. of supplementary angles Substitution Property Simplify Subtraction Property of Equality Division Property of Equality

6
**Properties of Congruence**

7
**Using Properties of Equality and Congruence**

What is the name of the property of equality or congruence that justifies going from the first statement to the second statement? A. 2x + 9 = 19 2x = 10 B. C. Subtraction Property of Equality Transitive Prop. Of Congruence Symmetric Property of Equality

8
**Proof A proof – a convincing argument that uses deductive reasoning.**

Logically shows why a conjecture is true. A two-column proof lists each statement on the left and the reasons on the right. Each statement must follow logically from the steps before it.

9
Proof

10
**Writing a Two-Column Proof**

Write a two-column proof. Given: Prove:

11
**Writing a Two-Column Proof**

12
More Practice!!!!! Homework – p. 117 – 118 # 5 – 19 ALL.

Similar presentations

OK

2.3 Diagrams and 2.4 Algebraic Reasoning. You will hand this in P. 88, 23.

2.3 Diagrams and 2.4 Algebraic Reasoning. You will hand this in P. 88, 23.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Download ppt on civil disobedience movement protest Ppt on channels of distribution diagram Ppt on human resources information system Ppt on e commerce business model Ppt on area of parallelogram worksheet Ppt on power transmission elements Ppt on programmable logic array Ppt on classical economics Ppt on polynomials in maths games Ppt on next generation 2-stroke engine parts