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.
