Daily Warm Up Quiz

Mrs. McConaughy Geometry 1

I. Complete each theorem below:

1.Vertical angles are ________________________________2.Linear pairs of angles are ____________________________3.If two angles are congruent and supplementary, then _______________________________________________________ .

II. Define:Complementary angle:___________________________________Supplementary angle; ___________________________________

III. Given the following diagram, nameA.All linear pairs of angles ____________________________B.All vertical angle pairs ____________________________

1315 17 19

Mrs. McConaughy Geometry 2

Introduction to Proof, Part 1

During this lesson, you will:

Identify premises for geometric argument Write simple proofs using Properties of Algebra & Properties of Equality

Mrs. McConaughy Geometry 3

Premises for Geometric Proof

1. Definitions and undefined terms2. Properties of algebra, equality, and

congruence3. Postulates of geometry4. Previously accepted or proven

geometric theorems

Mrs. McConaughy Geometry 4

Matching Review: Properties of Algebra

Column A__ Commutative Property of Addition__ Commutative Property of Multiplication__ Associative Property of Addition__ Associative Property of Multiplication__Distributive Property

Column Ba. a + b = b + ab. (a + b) + c = a + (b +

c)c. (ab)c = a(bc) d. ab = bae. a (b + c) = ab + ac

a

d

b

c

e

Mrs. McConaughy Geometry 5

Matching Review: Properties of Equality

__Reflexive Property of Equality__Symmetric Property of Equality__Addition Property of Equality__Subtraction Property of Equality__Multiplication Property of Equality__Division Property of Equality

1. a = a2. If a = b then b = a.3. If a = b, then a + c = b + c4. If a = b, then a * c = b * c5. If a = b, then a - c = b – c6. If a = b, then a / c = b / c (provided

c ≠ 0)

1.

3.

2.

4.

5.

6.

Mrs. McConaughy Geometry 6

Writing Simple Algebraic Proofs Using Properties of Algebra &

Equality

You use properties of algebra and equality to solve equations. When you solve an equation, you are writing an algebraic proof. Each step can be supported by a property.

Mrs. McConaughy Geometry 7

Example A: Given: 5x – 12 = 3 (x + 2) Prove: x = 9

Statement Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Mrs. McConaughy Geometry 8

Example B: If ax + b = c, then x = (c-b)/a; a ≠ 0.

Given: Prove:ax + b = c x = (c-b)/a

Statement Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Mrs. McConaughy Geometry 9

Final Checks For Understanding

If each statement in the first column is given information, for the corresponding conclusion?

Given ConclusionRT + LM = 19; LM = 7 RT= 12m AB = 25 2 (mAB) = 50AZ = 26 AZ/2 = 13

Mrs. McConaughy Geometry 10

Homework Assignment #1

Writing Simple Algebraic Proofs Supplemental WS, plus page 91-

92: 1, 2 3,