Section 2.4: Properties of Equality and Algebraic Proofs

1 / 13

# Section 2.4: Properties of Equality and Algebraic Proofs - PowerPoint PPT Presentation

Section 2.4: Properties of Equality and Algebraic Proofs. October 5, 2009. Addition. If a=b, then a + c = b + c If x – 5 = 7, then x = 12 Since x – 5 + 5 = 7 + 5 This can be used with Angles and Segments as well If &lt;A = &lt;B , then &lt;A + 90 = &lt;B + 90. Subtraction.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Section 2.4: Properties of Equality and Algebraic Proofs' - clarke-lambert

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Section 2.4: Properties of Equality and Algebraic Proofs

October 5, 2009

• If a=b, then a + c = b + c
• If x – 5 = 7, then x = 12
• Since x – 5 + 5 = 7 + 5
• This can be used with Angles and Segments as well
• If <A = <B , then <A + 90 = <B + 90
Subtraction
• If a=b, then a - c = b - c
• If x + 3 = 10, then x = 7
• Since x + 3 - 3 = 10 - 3
• This can be used with Angles and Segments as well
• If <A + <B = 180, then <A = 180 - <B
• Since <A + <B - <B = 180 - <B
Multiplication
• If a=b, then ac = bc
• If ½x = 5, then x = 10
• Since 2(½x) = 2(5)
• This can be used with Angles and Segments as well
• If <A = 45, then 2(<A) = 90
• Since 2(<A) = 2(45)
Division
• If a=b, then a / c = b / c (if c is not 0)
• If 4x = 12, then x = 3
• Since 4x / 4 = 12 / 4
• This can be used with Angles and Segments as well
• If 2AB = 20, then AB = 10
• Since 2AB / 2 = 20 / 2
Distributive
• If a ( b + c), then ab + ac
• If 2( x + 6) = 10, then 2x + 12 = 10
• This can be used with Angles and Segments as well
• If 3(AB + BC) = 21, then 3AB + 3BC = 21
Substitution
• If a = b and a = c, then b = c
• If x + 5 = y and x = 4, then y = 9
• Since 4 + 5 = y, so 9 = y and y = 9
• This can be used with Angles and Segments as well
• If <A + <B = 180 and <B = <C,

then <A + <C = 180

Reflexive, Symmetric, Transitive
• Reflexive:
• a = a
• x = x
• <A = <A
• Symmetric:
• If a = b, then b = a
• If x + 5 = 15, then 15 = x + 5
• If 90 = <A, then <A = 90
• Transitive:
• If a = b and b = c, then a = c
• If x + 5 = y, and y = 10, then x + 5 = 10
• If <A + <B = <C and <C = 90, then

<A + <B = 90

Practice – Name the Property of Equality
• If x + 5 = -11, then x = -16
• If AB+BC=AC and AC=10, then AB+BC=10
• If <C=90 and <B=90, then <C=<B
• If 3x + 5= 12, then x + 5/3 = 4
• If -2/3x = 4, then x = -6

### Homework – Practice Workbook 2.4 #1-8

Proofs
• Formal Proof – a two column proof of statements and reason which follows a step-by-step procedure to reach a conclusion. THESE ARE THE KIND WE WILL USE.
• There are also:
• Informal Proofs, which are a paragraph describing each step.
• Flow Proof, which show each step in a flow chart.
Formal Proofs

LOOK AT THE PROOFS ON PW 2-4.

You will always be given 2 things in a Formal Proof.

• Given: This is your 1st statement
• Prove: This is your last statement

Statement #2 is always based on what you are given.

Statements #3-5 are based on what additional things you need for your prove statement.