Unit 1 Test Flashcards
Is the converse of a statement necessarily true?
No
If you live in the Ozarks, then you live in the United States.
What is the hypothesis and what is the conclusion?
Hypothesis: If you live in the Ozarks
Conclusion: You live in the United States
Straight Angle (define)
An angle is straight iff its measure is 180 degrees
Obtuse Angle (define)
An angle is obtuse iff its measure is greater than 90 degrees and less that 180 degrees
Adjacent (define)
share a ray
Right Angle (define)
An angle is a right angle iff its measure is 90 degrees
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.
No
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
A
Statement: If it is raing then it is wet.
Contrapositive
if not b then not a (if it is not wet then it is not raining)
Space (define)
Set of all points
Collinear Points (define)
Points are collinear iff they are on the same line
Coplanar Points (define)
Points are coplanar iff they are on the same plane
Acute Angle (define)
an angle is actue iff its measure is less that 90 degrees
Decide if the statement is a good definition by determining whether or not their converses are true: Dry ice is frozen carbon dioxide.
Yes; It is frozen carbon dioxide if and only if it is dry ice.
It is cold outside if it is snowing
What is the hypothesis and what is the conclusion?
Hypothesis: If it is snowing
Conclusion: It is cold outside
Statement: If it is raing then it is wet.
Inverse
if not a then not b (if not raining then not wet)
Midpoint (define)
A point is a midpoint of a segment iff it divides the segment into 2 congruent segments or 2 quual lengths
Congruent (define)
Segments are congruent iff theit lengths are equal
In Betweeness of Points (define)
A-B-C iff they are collinear and AB + BC = AC
Noncollinear Points (define)
Points are not collinear iff they are not on the same line
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
C
Postualtes (define)
A statement that is accepted to be true w/o proof
Noncoplanar Points
Points are not coplanar iff they are not on the same plane
Statement: If it is raing then it is wet.
Converse
if a then b (if wet then it is raining)
In the statement “If a then b” what do the letters “a” and “b” represnt?
a: hypothesis
b: conclusion
What is a statement that can be represented sybolically by “If a, then b” called?
Condition Statement
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.
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.
Betweeness of Rays (define)
Rays OA-OB-OC iff they are coplanar and the measure of angle AOB + the measure of angle BOC = the measure of angle AOC
Congruent Angles (define)
Angles are concgurent iff their measures are equal
Bisector/Midray
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)
Postulate 5 (define)
- Al line contains at least 2 points
- A plane contains at least 3 noncollinear points
- Space contains at least 4 noncoplanar points
Postulate 6 (define)
- Through any two points there is EXACTLY 1 line
- 2 points determine a line
Postulate 7 (define)
- 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
Postulate 8 (define)
- If 2 points are in a plane, then the line that contains them is also on the plane
Postulate 9 (define)
- If 2 places intersects, then their intersection is a line
Theorem 1-1 (define)
If two lines intersect, then they intersect in exactly one point.
Theorem 1-2 (define)
Through a line and a point not in the line there is exactly one plane
Theorem 1-3 (define)
If two lines intersect, then exactly one plane contains the lines
