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Inductive vs.

Deductive

ProofsJustify!Condi-tionals Definitions

Conditionals - 100Identify the hypothesis of the following conditional statement:

If mABC = 20, then ABC is an acute angle.

Answer: mABC = 20.

Conditionals - 200State the converse of this conditional:

If mABC = 20, then ABC is an acute angle.

Answer: If ABC is an acute angle, then mABC = 20.

Conditionals - 300

Conditionals - 400Provide a counterexample to demonstrate why the converse of this statement is false.

If mABC = 20, then ABC is an acute angle.

Answers may vary: mABC could equal any number between 0 and 90.

Conditionals - 500

Rewrite the definition of complementary angles as a

biconditional statement.Complementary angles – two

angles whose measures sum to 90°.

Answer: Angles are complementary if and only if the sum of their measures is 90°.

Definitions - 100

Definitions - 200State the definition of perpendicular lines.

Answer: Perpendicular lines are intersecting lines that meet to form right angles.

Definitions - 300State the definition of a right angle.

Answer: A right angle is an angle that measures 90°.

Definitions - 400Which of the following is the definition of a midpoint:A.) If point B is the midpoint of AC, then AB = BC.B.) If point B is the midpoint of AC, then AB = ½AC.C.) If point B is the midpoint of AC, then DB bisects AC.D.) If BX bisects ABC, then ABX XBC.

Answer: A: If point B is the midpoint of AC, then AB = BC.

Definitions - 500

What is the reason that you could use in a proof to justify that 1 2.

12

Answer: Vertical Angle Theorem – “Vertical Angles are Congruent.”

Justify! - 100Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated.

B

D

C F

GX1

3 2DX + XF = DF

Answer: Segment Addition Postulate.

Justify! - 200

Justify! - 300Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated.

B

D

C F

GX1

3 2

If CXF and DXG are supplementary, then mCXF + mDXG = 180

Answer: Def. of Supplementary Angles.

Justify! - 400Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated.

B

D

C F

GX1

3 2

If mBXD + mDXG = mFXG + mDXG, then mBXD = FXG.

Answer: Subtraction Property.

Justify! - 500Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated.

B

D

C F

GX1

3 2

If XF bisects CXG, then mCXF = ½mCXG.

Answer: Angle Bisector Theorem.

Proofs - 100Fill in the missing piece to the proof.

Statements Reasons1. m1 = m2 1. Given2. m1 = m3 2. Vertical Angles are 3. ___________ 3. Substitutionm2 = m3

Proofs - 200 Fill in the missing pieces to the proof.

123

4

A

B C

Given: mABC =mACB, m1 = m3

Prove: m2 = m4

Statements Reasons1. mABC =mACB 12. m1 + m2 = mABC m3 + m4 = mACB 23. m1 + m2 = m3 + m4 34. m1 = m3 45. m2 = m4 5

Given Add. Post.SubstitutionGivenSubtraction

Proofs - 300 Fill in the missing pieces to the proof.

AB C

D

X

1 2 3Given: mAXC = mBXD Prove: m1=m3

Statements Reasons1. mAXC = mBXD 1. Given2. ____________________ 2. Add. Postulate ____________________3. m1 + m2 = m2 + m3 3. _____________4. m1 = m3 4. _____________

m1 + m2 = mAXCm2 + m3 = mBXD

SubstitutionSubtraction

Proofs - 400

Proofs - 500 Complete the proof.

Statements Reasons

A B C

FED

Given: AC = DF; AB = EFProve: BC = DE

1. AC = DF2. AB + BC = AC DE + EF = DF

3. AB + BC = DE + EF4. AB = EF5. BC = DE

1. Given

2. Segment Addition Postulate

3. Substitution4. Given5. Subtraction

Inductive vs. Deductive - 100You notice that the 6 pentagons you have drawn on your paper has interior angle measures that add up to 540°. You conclude that all pentagons have interior angle measures that add up to 540°.

Answer: Inductive

Inductive vs. Deductive - 200When you complete a proof what type of reasoning are you applying?

Answer: Deductive

Inductive vs. Deductive - 300

Inductive vs. Deductive - 400When you complete an experiment that consists of making observations and then drawing conclusions, what type of reasoning are you applying?

Answer: Inductive

Inductive vs. Deductive - 500Just for fun…Look for a pattern and predict the next two numbers in the sequence.12, 14, 18, 24, ____, ____, …

Answer: 32, 42

FINAL JEOPARDY

• Category: Planning a Proof

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