Geometry Section 2.6 - Prove statements about segments and angles What the student should get from this: 1. Write two-column proofs 2. Prove geometric theorems by using deductive reasoning Donʼt forget these things! Properties of Equality

Mathematical Statement

Addition Property of Equality

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

Subtraction Property of Equality

If a = b, then a ! c = b ! c

Multiplication Property of Equality

If a = b, then ac = bc

Division Property of Equality

If a = b, and c ≠ 0, then

a b = c c

Reflexive Property of Equality

a=a

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

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

Substitution Property of Equality

If a = b, then b can be substituted for a in any expression

Letʼs go right at it! You must very quickly learn definitions, basic geometric properties, rules (postulates) and theorems. This is how it works... m

Given: intersecting lines m and n Prove: !1 " !3 Statements

2 1

3

Reasons

n

Brainstorm Area (BSA)

Example: Given: !ABC is a right angle Prove: !ABD and !DBC are complementary angles Statements

A D

Reasons 1 2 C

B Brainstorm Area (BSA)

Example: 1

Given: !1 is supplementary to !2 # !1 is supplementary to !3 Prove: !2 " !3 Statements

Reasons

3

Brainstorm Area (BSA)

2

Lastly... you should be able to solve problems based on the mathematical symbols. Example:

(2x + 3.5)˚

(3x + 1.5)˚

(2.5x ! 5)˚

How do you do a proof?

Assignment: p.116 #s 5-10 all, 17-18, 21-27 all. Show work. Draw all pictures. Bon chance! Due next period.