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Inductive vs. Deductive ProofsJustify! Condi- tionals Definitions
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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
• Place your wagers!