Midpoint
Distance
Conditional Statements
Direct Proof
Indirect Proof
100
What is the midpoint of a segment?
The middle point of the segment.
100
Point A is at coordinate 4 and Point B is at coordinate 17 - what is the distance between points A and B?
13 units.
100
What is the hypothesis in the following statement:
If today is Friday, then tomorrow is Saturday.
Today is Friday
100
What is always your first step in a two-column proof?
The Given Statement.
100
What is the first step of an indirection proof by contrapositive?
Assume ~q is true.
200
What is the midpoint of (2, 4) and (6, 8)?
(4, 6)
200
Point A is at coordinate -11 and Point B is at coordinate 8 - what is the distance between points A and B?
19 units.
200
What is the converse of the following statement:
If today is Tuesday, then tomorrow is Wednesday.
If tomorrow is Wednesday, then today is Tuesday.
200
What property justifies step 2?
1) 3(x-4)+2=11
2) 3x-12+2=11
3) 3x-10=11
4) 3x=21
5) x=7
Distributive Property
200
What is the second step of an indirect proof by contradiction?
Show that the assumption ~q leads to a contradiction.
300
What is the midpoint of (-5, -7) and (9, -3)?
(2, -5)
300
What is the distance formula?
300
What is the inverse of the following statement:
If tomorrow is Thursday, then today is Wednesday.
If tomorrow is not Thursday, then today is not Wednesday.
300
Below is the "statements" column, complete all 5 steps of the "reasons" column.
1) 3(x-4)+2=11
2) 3x-12+2=11
3) 3x-10=11
4) 3x=21
5) x=7
1) Given
2) Distributive Property
3) Substitution PoE
4) Addition PoE
5) Division PoE
300
Use indirect reasoning to draw a conclusion from the situation:
Jordan only hunts during the weekends of fall. Jordan hunted last weekend.
It is fall.
400
What is the midpoint between (-2, -9) and (-3, 4)?
(-2.5, -2.5)
400
What is the distance between A(-2, 3) and B(4, 14)?
Approximately 12.5 (square root of 157)
400
Write the contrapositive of the following statement:
If the Vikings win, they will go to the Super Bowl.
If the Vikings do not go to the Super Bowl, they did not win.
400
Complete the two column proof for the following given:
Given: 4x-17=-6x+13
Statements: Reasons:
1) 4x-17=-6x+13 1) Given
Following steps may vary.
400
What is your first step for an indirect proof of the following conditional:
If a whole number is between 1 and 4, then it is a factor of 6.
Assume that if a whole number is between 1 and 4, then it is not a factor of 6.
500
If (3, 7) is the midpoint, and on of the endpoints is (4, 9) what is the other endpoint?
(2, 5)
500
What is the EXACT distance between A(-3, 7) and B(2, 12)?
5(sqrt5)
500
Create a conditional statement and write the inverse, converse and contrapositive.
Answers vary.
500
Create your own two column proof that consists of at least 5 steps.
Answers vary.
500
Write an indirect proof of the following by using proof by contradiction:
If Jordan walks more than 8 km over a two-day period, then she walks more than 4 km on one or both days.
Step 1) Assume Jordan does not walk more than 4 km on either day.
Step 2) If Jordan does not walk more than 4 km on either day, then the total distance he walks over the two-day period must be less than or equal to 8 km. This contradicts the hypothesis.
Step 3) Because the assumption leads to a contradiction, Jordan must then walk more than 4 km on one or both days.