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) B)7 C)9 D)17 E)

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: m1 + m2 = m4

Prove: m3 + m1 + m2 = 180° Paragraph Proof: It is given that m1 + m2 = m4. 3 and 4 are supplementary by the Linear Pair

Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 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, mWXY = 90° by the definition of a right angle. By the Angle Addition Postulate, mWXY = m2 + m3. By substitution, m2 + m3 = 90°. Since 1 3, m1 = m3 by the definition of congruent angles. Using substitution, m2 + m1 = 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. mWXY = 90° 2. Def. of right angle 3. m2 + m3 = mWXY 3. Angle Add. Postulate 4. m2 + m3 = 90° 4. Subst. 5. 1 3 5. Given 6. m1 = m3 6. Def. of s 7. m2 + m1 = 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

m3 + m4 = 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.