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C HAPTER 2 2-7 flow charts and paragraph proof. SAT P ROBLEM OF THE DAY.

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Presentation on theme: "C HAPTER 2 2-7 flow charts and paragraph proof. SAT P ROBLEM OF THE DAY."— Presentation transcript:

1 C HAPTER flow charts and paragraph proof

2 SAT P ROBLEM OF THE DAY

3 SAT P ROBLEM OF THE DAY SOLUTION Right Answer: D

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

5 F LOW 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 T HEOREM

7 E XAMPLE #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 C ONTINUE Two-column proof:

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

14 SOLUTION Flowchart proof:

15 S TUDENT GUIDED PRACTICE Do problems 7 and 8 from your book page 123

16 P ARAGRAPH 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 T HEOREMS

18 E XAMPLE 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 S OLUTION

20 E XAMPLE #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 S OLUTION 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 E XAMPLE 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 S OLUTION Paragraph:

24 S TUDENT GUIDED P RACTICE Do problems in the book page 123 and124

25 H OMEWORK !! Do problems 3-5 on you book page 122

26 C LOSURE 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.


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