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

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

SAT Problem of the day solution Right Answer: D

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

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.

Theorem

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.

continue Flowchart proof:

continue Two-column proof:

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

continue Flowchart proof:

Continue Two-column proof:

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

solution Flowchart proof:

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

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.

Theorems

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°.

Solution

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.

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

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.

Solution Paragraph:

Student guided Practice Do problems 8 -10 in the book page 123 and124

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

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.