Writing ProofsDuring this lesson, you will:

Write reasons for statements Write simple geometric proofs using properties of equations

Recall: Properties of Equations

Addition: If a = b, then a + c = b + c, for all real numbers a, b, and c. Subtraction: If a = b, then a - c = b - c, for all real numbers a, b, and c. Multiplication: If a = b, then a ∙ c = b ∙ c, for all real numbers a, b, and c. Division: If a = b, then a/c = b/c.

Example 1What reason can you give for the

following conclusion? If m ∠ AOB = m ∠ COD,then m ∠ AOB + m ∠ BOC = m ∠ BOC + m ∠ COD

Addition Property of Equality

?

Example 2

What reason can you give for the following conclusion?

If 2 (m ∠P )= 80, then m ∠P = 40.

Division Property of

Equality

Example 3

What conclusion can you draw based upon the given information? Give a reason for each statement.Given: OP bisects AOB

Prove: AOP POB

uur

OP bisects AOBuur

Statement Reason

1.

2.

1.

2.

Given.

Example 4 Write a complete proof of the following:Given: m ∠ x = 38; m ∠ y = 38 Prove: x y

Statement Reason

1. 2. 3. 4.

1.2.3.4.

Example 5

Give a reason for each step in the proof on the following slide.

Given: m ∠AOB + m∠ BOC = m ∠BOC + m ∠

CODProve: ∠ AOB ∠ COD

Example 5

Statement Reason1. 2. 3. 4.

1.2.3.4.

Example 6

1. Draw and label a diagram based upon the given information.

2. Write the missing statements in the proof on the following slide.

Directions:

Given: AB ≅ BC, BC ≅ CD, AB = 21

Prove: CD = 21 Diagram:

A B C D

STATEMENT REASON

1. AB ≅ BC 1.

2. BC ≅ CD 2.

3. _______ 3.

4. AB = CD 4.

5. AB = 21 5.

6. 6.

Final Checks for Understanding

On the following slide, statements in the first

column are given information. Use these to draw logical conclusion,

then justify your reason for each corresponding

conclusion.

Statement Reason

1. XY = ZW and ZW = AB; AB = 92. 3.

1. AB = CD and AB = 82.

1. XYZ ABC and ABC RPG2.

1. Given2.3.

1. Given2.

1. 2.

Final Checks for Understanding

Final Checks for Understanding

Statement Reason

1. m ROA = m POW ; m POW = 782.

1. RT + LM = 19; LM = 122. RT + 12 = 19

1. Given2.

1. Given

2.

Final Checks for Understanding

Statement Reason

1. m SLC + m RTU = 127; m SLC = 182. 3. m RTU = 109

1. AB = CD and AB = 82.

1. m BIG = 83 2 (m BIG) = 166

1. Given

2. 3.

1. Given2.

1. 2.

Final Checks for Understanding

Statement Reason

1. m 1 + m 2 = m 2 + m 3 ;

2. m 2 = m 2 3. m 1 = m 3

1. HO + OT = OT + DG2. OT= OT3. HO = DG

1. Given2.3.

1. Given2. 3.

HOMEWORK ASSIGNMENT

Writing Simple Geometric Proofs WS