1. 2-7 flow charts and paragraph proof
Chapter 2
2-7 flow charts and paragraph proof

2. SAT Problem of the day
The distance between two points (-3,5)and (-3,- 12) is
A)√17
B)7
C)9
D)17
E)√60

3. SAT Problem of the day solution
Right Answer: D

4. Objectives Write flowchart and paragraph proofs.
Prove geometric theorems by using deductive reasoning.

5. Flow chart
A second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof.
The justification for each step is written below the box.

6. Theorem

7. Example#1 Use the given flowchart proof to write a two- column proof.
Given: 2 and 3 are comp.
1  3
Prove: 2 and 1 are comp.

8. continue
Flowchart proof:

9. continue
Two-column proof:

10. example#2 Use the given flowchart proof to write a two- column proof.
Given: RS = UV, ST = TU
Prove: RT  TV

11. continue
Flowchart proof:

12. Continue
Two-column proof:

13. Example#3 Use the given two-column proof to write a flowchart proof.
Given: B is the midpoint of AC.
Prove: 2AB = AC

14. solution
Flowchart proof:

15. Student guided practice
Do problems 7 and 8 from your book page 123

16. Paragraph proofs What are paragraph proofs?
A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.

17. Theorems

18. Example Use the given paragraph proof to write a two- column proof.
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Paragraph Proof: It is given that
m1 + m2 = m4. 3 and 4 are
supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°.

19. Solution

20. Example#2 Use the given paragraph proof to write a two- column proof.
Given: WXY is a right angle. 1  3
Prove: 1 and 2 are complementary.
Paragraph Proof: Since WXY is a right angle, mWXY = 90° by the definition of a right angle. By the Angle Addition Postulate, mWXY = m2 + m3. By substitution, m2 + m3 = 90°. Since 1  3, m1 = m3 by the definition of congruent angles. Using substitution, m2 + m1 = 90°. Thus by the definition of complementary angles, 1 and 2 are complementary.

21. Solution Statements Reasons 1. WXY is a right angle. 1. Given
2. mWXY = 90°
2. Def. of right angle
3. m2 + m3 = mWXY
3. Angle Add. Postulate
4. m2 + m3 = 90°
4. Subst.
5. 1  3
5. Given
6. m1 = m3
6. Def. of  s
7. m2 + m1 = 90°
7. Subst.
8. 1 and 2 are comp.
8. Def. of comp. angles

22. Example Use the given two-column proof to write a paragraph proof.
Given: 1 and 2 are complementary
Prove: 3 and 4 are complementary
m3 + m4 = 90°
3 and 4 are comp.

23. Solution
Paragraph:

24. Student guided Practice
Do problems in the book page 123 and124

25. Homework !!
Do problems 3-5 on you book page 122

26. Closure
Today we learned about flowcharts , two column paragraphs and how to use them to make proofs.
Next class, we are going to start with chapter 3.