2.4 & 2.5 GeometryBrett Solberg AHS ‘11-’12

Warm-upSolve for x

◦2(x – 5) = -4

Solve for x

Today’s ObjectivesLink reasoning to algebra and

geometry.

Justify steps of math.

No Name Basket/Missing Assignments

Mr. Fix-ItWho is Mr. Fix-It?

What tools does he need to do his job?

Tools For MathTo reach conclusions we’ll use:

◦Inductive/Deductive Reasoning◦Properties◦Postulates◦Theorems

Addition PropertyIf a = b, then a + c = b + c.

Examples◦If 2 = 2, then 2 + 4 = 2 + 4.◦If x – 2 = 4, then x – 2 + 2 = 4 + 2

Subtraction PropertyIf a = b, then a – c = b – c.

Examples◦If 4 = 4, then 4 – 2 = 4 – 2.◦If x + 6 = 10, then x + 6 – 6 = 10 –

6.

Multiplication PropertyIf a = b, then a*c = b*c

Examples◦If 4 = 4, then 4*3 = 4*3◦If x = 3, then *2x = 3*2

Division PropertyIf a = b and c not equal o, then

a/c = b/c.If 7 = 7, then = .If 4x = 16, then = .

Distributive Propertya(b + c) = ab + ac

2(x + 1) = 2x + 2

x(x – 5) = x2 – 5x

Reflexive Propertya = a

2 = 2

∠a = ∠a

Symmetric PropertyIf a = b, then b = a.

4 = 4

If 2x = 6, then 6 = 2x.

Biconditional

Transitive PropertyIf a = b and b = c, then a = c.

If angle a = 45, and angle b = 45, then a = b.

Law of Syllogism

Substitution PropertyIf a = b, then b can replace a.

Angle A and B are complimentaryAngle A = 2x + 1 Angle B =

4x2x + 1 +4x = 90

Theorems and DefinitionsYou can use definitions and

theorems to help reach conclusions.

M is the midpoint of AB.AM congruent to MB by

definition.

Using Your ToolsSolve for x

◦4x – 2 = 10◦ +2 +2 Addition

Property◦4x = 12◦/4 /4 Division

Property◦x = 3

Justify Each StepSolve For x∠CDE & ∠EDF are

supplementaryx + (3x + 20) =

1804x + 20 = 1804x = 160x = 40

Angle Addition Post.

Substitution Property

SimplifySubtraction

PropertyDivision Property

Example 2 Prove x = 6AB = 2x, BC = 3x – 9, AC = 21 GivenAB + BC = AC Segment

Addition Postulate

2x + 3x – 9 = 21 Substitution5x – 9 = 21 Simplify5x – 9 + 9 = 21 + 9 Addition

Property5x = 30 Simplify5x/5 = 30/5 Division

Propertyx = 6

TheoremA statement that you prove to be

true.

Vertical Angles TheoremVertical Angles are Congruent.∠1 ≅ ∠3∠2 ≅ ∠4

Given: ∠1 and ∠2, ∠3 and ∠2 are supplementary

Prove ∠1 ≅ ∠3

∠1 + ∠ 2 = 180 given∠3 + ∠2 = 180 given∠1 + ∠2 = ∠2 + ∠3 substitution∠1 = ∠3 subtraction

Homework2-4 Worksheet2-5 pg. 112 #1-13 on back of

worksheet