Unit 1 Test

Question 1

Is the converse of a statement necessarily true?

Answer 1

No

Question 2

If you live in the Ozarks, then you live in the United States.

What is the hypothesis and what is the conclusion?

Answer 2

Hypothesis: If you live in the Ozarks

Conclusion: You live in the United States

Question 3

Straight Angle (define)

Answer 3

An angle is straight iff its measure is 180 degrees

Question 4

Obtuse Angle (define)

Answer 4

An angle is obtuse iff its measure is greater than 90 degrees and less that 180 degrees

Question 5

Adjacent (define)

Answer 5

share a ray

Question 6

Right Angle (define)

Answer 6

An angle is a right angle iff its measure is 90 degrees

Question 7

Decide if the statement is a good definition by determining whether or not their converses are true: If it is New Year’s Day, then it is a holiday.

Answer 7

No

Question 8

Draw an Euler diagram to represnt the following statement:

All athletes who compete in the Olympics are amateurs.

Which of the following statements are illustrated by your diagram?
a) If an athlete competes in the Olymics, then the athlete is an amateur.
b) If an athlete is an amateur, then the athlete competes in the Olympics.
c) If an athlete does not compete in the Olympics, then the athlete is not an amateur.
d) If an athlete is not an amateur, then the athlete does not compete in the Olympics

Answer 8

A

Question 9

Statement: If it is raing then it is wet.
Contrapositive

Answer 9

if not b then not a (if it is not wet then it is not raining)

Question 10

Space (define)

Answer 10

Set of all points

Question 11

Collinear Points (define)

Answer 11

Points are collinear iff they are on the same line

Question 12

Coplanar Points (define)

Answer 12

Points are coplanar iff they are on the same plane

Question 13

Acute Angle (define)

Answer 13

an angle is actue iff its measure is less that 90 degrees

Question 14

Decide if the statement is a good definition by determining whether or not their converses are true: Dry ice is frozen carbon dioxide.

Answer 14

Yes; It is frozen carbon dioxide if and only if it is dry ice.

Question 15

It is cold outside if it is snowing

What is the hypothesis and what is the conclusion?

Answer 15

Hypothesis: If it is snowing

Conclusion: It is cold outside

Question 16

Statement: If it is raing then it is wet.
Inverse

Answer 16

if not a then not b (if not raining then not wet)

Question 17

Midpoint (define)

Answer 17

A point is a midpoint of a segment iff it divides the segment into 2 congruent segments or 2 quual lengths

Question 18

Congruent (define)

Answer 18

Segments are congruent iff theit lengths are equal

Question 19

In Betweeness of Points (define)

Answer 19

A-B-C iff they are collinear and AB + BC = AC

Question 20

Noncollinear Points (define)

Answer 20

Points are not collinear iff they are not on the same line

Question 21

The ball is out of play when it completely crosses the goal line.

Which of the following staements must be true?
a) If the ball completely crosses the goal line, then it is out of play.
b) The ball is out of play if it has completely crossed the goal line
c) The ball is out of play only if it has completely crossed the goal line

Answer 21

C

Question 22

Postualtes (define)

Answer 22

A statement that is accepted to be true w/o proof

Question 23

Noncoplanar Points

Answer 23

Points are not coplanar iff they are not on the same plane

Question 24

Statement: If it is raing then it is wet.
Converse

Answer 24

if a then b (if wet then it is raining)

Question 25

In the statement “If a then b” what do the letters “a” and “b” represnt?

Answer 25

a: hypothesis

b: conclusion

Question 26

What is a statement that can be represented sybolically by “If a, then b” called?

Answer 26

Condition Statement

Question 27

Reorganize the proofs so that they are easier to follow.

Theorm: If the is no Great Pumpkin, Snoop won’t have pie for dinner.

Proof:
If Lucy plays a trick on Charlie Brown, he will be upset.
If Linus is mistaken, Lucy is pleased.
If Lucy becomes unruly, she plays a trick on Charlie Brown.
If there is no Great Pumpkin, then Linus is mistaken.
If Charlie Brown forgets to feed Snoopy, Snoopy won’t have pie for dinner.
If Lucy is pleased, she becomes unruly.
Charlie Brown forgets to feed Snoopy if he is upset.

Answer 27

If there is no Great Pumpkin, then Linus is mistaken.
If Linus is mistaken, Lucy is pleased.
If Lucy is pleased, she becomes unruly.
If Lucy becomes unruly, she plays a trick on Charlie Brown.
If Lucy plays a trick on Charlie Brown, he will be upset.
Charlie Brown forgets to feed Snoopy if he is upset.
If Charlie Brown forgets to feed Snoopy, Snoopy won’t have pie for dinner.

Question 28

Betweeness of Rays (define)

Answer 28

Rays OA-OB-OC iff they are coplanar and the measure of angle AOB + the measure of angle BOC = the measure of angle AOC

Question 29

Congruent Angles (define)

Answer 29

Angles are concgurent iff their measures are equal

Question 30

Bisector/Midray

Answer 30

A ray is a midray of an angle iff it divides the angle into 2 congruent angles or into 2 equal measures (A ray is a bisector of an angle)

Question 31

Postulate 5 (define)

Answer 31

• Al line contains at least 2 points
• A plane contains at least 3 noncollinear points
• Space contains at least 4 noncoplanar points

Question 32

Postulate 6 (define)

Answer 32

• Through any two points there is EXACTLY 1 line
• 2 points determine a line

Question 33

Postulate 7 (define)

Answer 33

• Through any 3 points, there is at least 1 plane
• Through any 3 noncollinear points, there is EXACTLY 1 plane
• 3 noncollinear points determine a plane

Question 34

Postulate 8 (define)

Answer 34

• If 2 points are in a plane, then the line that contains them is also on the plane

Question 35

Postulate 9 (define)

Answer 35

• If 2 places intersects, then their intersection is a line

Question 36

Theorem 1-1 (define)

Answer 36

If two lines intersect, then they intersect in exactly one point.

Question 37

Theorem 1-2 (define)

Answer 37

Through a line and a point not in the line there is exactly one plane

Question 38

Theorem 1-3 (define)

Answer 38

If two lines intersect, then exactly one plane contains the lines