Inductive Reasoning
Determine whether each conjecture is true or false. Find a counterexample for any false conjecture.
If x is an integer, then –x is a negative number.
False; sample answer: Suppose x = –1, then –x = 1.
Use the statements to write a compound statement for each conjunction or disjunction. Then find the truth values. Explain your reasoning.
p: -7+3=-4
q: The sum of complementary angles is 90°.
r: 3-4=-1
p and q
-7 + 3 = -4 and the sum of complementary angles is 90°; p is true, and q is true, so p and q is true.
What is the first thing you should do when you walk in class?
- Bell ringer/ Warmup
- Write Agenda
- Look at what materials are needed for the day
-Absolutely NOT play around or get on the phone.
Determine whether each conclusion is based on inductive or deductive reasoning.
Everybody who goes to camp must have a physical exam. Carl goes to camp. Carl had a physical exam.
deductive
This postulate states that If two planes intersect, then their intersection is a line.
Postulate 3.7
Make a conjecture about each value or geometric relationship.
the relationship between x and y if x + y = 0.
x = –y
Identify the hypothesis and conclusion of each conditional statement.
If your clothes are wet, then you walked in the rain.
H: your clothes are wet; C: you walked in the rain
Triangle ABC has vertices A, B, and C. Under which transformations is AB = A′B′?
A. Translation 5 units left
B. Rotation 180° clockwise about A
C. Reflection in the line through
D. All of the above
All of the above
Determine whether each conclusion is based on inductive or deductive reasoning.
A café owner notices that she usually has more customers at noon. It is 11:45, so she anticipates that she will have more customers soon.
inductive
This postulate states that If two points lie in a plane, then the entire line containing those points lies in that plane.
Postulate 3.5
Make a conjecture about each value or geometric relationship.
the relationship between the angles of a rectangle
All the angles are congruent.
Write the conditional and converse for each statement.
The school cafeteria will be closed if there is a school holiday.
Conditional: If there is a school holiday, then the school cafeteria will be closed. The conditional is true.
Converse: If the school cafeteria is closed, then there is a school holiday.
B is between A and C. If AB = x + 2, BC = 2x - 3 and AC = 5x-7, what is AB?
AB = 5
Determine whether each conclusion is valid based on the given information. Write valid or invalid. Explain your reasoning.
Given: If you eat at a restaurant, then you will spend money. You spend money.
Conclusion: You are eating at a restaurant.
Invalid; You might be spending money somewhere else.
What are the three ways you can write a proof?
1. Two-column proof
2. Flow proof/ flow chart proof
3. Paragraph Proof
Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the next term in the sequence.
2, 4, 8, 16, 32
Each term in the pattern is two times the previous term;
The next term is 64
Write the converse. Determine whether each related conditional is true or false
If José has eight dinner plates, then he can serve eight people at his dinner party.
Converse: If eight people can be served at his dinner party, then José has eight dinner plates. The converse is true.
What is the length of PS, when R is the midpoint of PS?
PR = 7x - 5
RS = 4(x + 1)
PS = 32
Use the Law of Syllogism to draw a valid conclusion from each set of given statements, if possible. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
If Camila drives too fast, then she will get another speeding ticket.
If Camila gets another speeding ticket, then she will lose her driver’s license.
If Camila drives too fast, then she will lose her license.
Determine whether each statement is always, sometimes, or never true. Justify your argument.
Points A and B determine a plane.
Never; Two points determine a line. It takes three noncollinear points to determine a plane. Postulate 3.2 states that through any three noncollinear points, there is exactly one plane.
Make a conjecture about each value or geometric relationship.
the product of two and a whole number, plus two
The result is even.
Write each biconditional as a conditional and its converse.
A soccer ball will bounce if and only if it is inflated with air.
Conditional: If a soccer ball bounces, then it is inflated with air.
Converse: If a soccer ball is inflated with air, then it will bounce.
Two angles are complementary. The measure of the larger angle is 6 degrees less than 3 times the measure of the smaller angle.
What are the measures of the smaller and larger angles?
Smaller Angle = 24
Larger Angle = 66
Use the Law of Syllogism to draw a valid conclusion from each set of given statements, if possible. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
If a baseball player hits a ball over the fence, then he scores a home run.
If an outfielder catches the ball, the baseball player is out.
No valid conclusion; The conclusion of statement (1) is not the hypothesis of statement (2).
What reasons are missing in this two column proof?
Given: GH=JK; GH= 7x-32 and JK=6x+26
Prove: x = 58
Statements (Reasons)
1. GH = JK (Given)
2. 7x – 32 = 6x + 26 (___________________)
3. 7x = 6x + 58 (Addition Property of Equality)
4. x = 58 (___________________________)
2. Substitution
4. Subtraction Property of Equality