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Writing Proofs. During 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. - PowerPoint PPT Presentation
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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
