Geometry

Section 2.6 - Prove statements about segments and angles

What the student should get from this:1. Write two-column proofs2. 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 EqualityIf a = b, and c ≠ 0, then

ac=bc

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...

Given: intersecting lines m and nProve: !1 " !3

Brainstorm Area (BSA)

12

3

m

nStatements Reasons

Example:

Given: !ABC is a right angle

Prove: !ABD and !DBC are complementary angles

Example:

Given: !1 is supplementary to !2# !1 is supplementary to !3

Prove: !2 " !3

Statements Reasons

Brainstorm Area (BSA)

A

B C

D

1

2

Statements Reasons

Brainstorm Area (BSA)

1 2

3

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

Example:

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.

(2x + 3.5)˚(3x +1.5)˚

(2.5x ! 5)˚