Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric...
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Transcript of Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric...
![Page 1: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/1.jpg)
Writing ProofsDuring this lesson, you will:
Write reasons for statements Write simple geometric proofs using properties of equations
![Page 2: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/2.jpg)
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.
![Page 3: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/3.jpg)
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
?
![Page 4: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/4.jpg)
Example 2
What reason can you give for the following conclusion?
If 2 (m ∠P )= 80, then m ∠P = 40.
Division Property of
Equality
![Page 5: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/5.jpg)
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.
![Page 6: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/6.jpg)
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.
![Page 7: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/7.jpg)
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
![Page 8: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/8.jpg)
Example 5
Statement Reason1. 2. 3. 4.
1.2.3.4.
![Page 9: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/9.jpg)
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:
![Page 10: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/10.jpg)
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.
![Page 11: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/11.jpg)
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.
![Page 12: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/12.jpg)
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
![Page 13: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/13.jpg)
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.
![Page 14: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/14.jpg)
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.
![Page 15: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/15.jpg)
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.
![Page 16: Writing Proofs During this lesson, you will: Write reasons for statements Write simple geometric proofs using properties of equations.](https://reader035.fdocuments.us/reader035/viewer/2022062721/56649f1e5503460f94c35052/html5/thumbnails/16.jpg)
HOMEWORK ASSIGNMENT
Writing Simple Geometric Proofs WS