Vocabular Words Flashcards
Unit 1 -
Space
Set of all points
Collinear points
Points are collinear iff they are on the same line
Coplanar points
Points are coplanar iff they are on the same plane
Noncollinear points
Points are not collinear iff they are not on the same line
Noncoplanar points
Points are not coplanar iff they are not on the same plane
Postulates
A statement that is accepted to be true without proof
(Def.) In Betweeness of Points
B is between A and C iff they are collinear + the distance from A to B plus the distance from B to C equals the distance from A to C.
Shorter Version: A-B-C iff they are collinear and AB + BC = AC
(Def.) Midpoint
A point is a midpoint of a segment iff it divides the segment into 2 congruent segments or 2 equal lengths + collinear to the other points
(Def.) Congruent Segments
Segments are congruent iff their lengths are equal
(Def.) Acute angle
An angle is acute iff its measure is less that 90 degrees
(Def.) Right angle
an angle is a right iff its measure is 90 degrees
(Def.) Obtuse angle
An angle is obtuse iff its measure is greater than 90 degrees and less that 180 degrees
(Def.) Straight angle
an angle is a straight angle iff its measure is 180 degrees
(Def.) Adjacent
share a ray
(Def.) Betweeness of Rays
Ray OA - Ray OB - Ray OC iff they are coplanar and the measure of (m <AOB) + measure of (m <BOC) = measure of (m <AOC)
(Def.) Congruent angles
Angles are congruent iff the measures are equal
(Def.) Midray
A ray is a midray of an angle iff it divides the angle into 2 congruent angles or into 2 equal measures
(Def.) Complementary Angles
2 angles are complementary iff the sum of their measures is 90 degrees
(Def.) Supplementary Angles
2 angles are supplementary iff the sum of their measures is 180 degrees
(Def.) Perpendicular Lines
Lines are perpendicular iff they form right angles
Postulate 5
- A line contains at least 2 points
- A plane contains at least 3 noncollinear points
- Space contains at least 4 noncoplanar points
Postulate 6
- Through any 2 points there is exactly 1 line
- 2 points determine a line
Postulate 7
- 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 9
If 2 planes intersect, then their intersection is a line
Postulate 8
If 2 points are in a plane, then the line that contains them is also on the plane
Theorem 1-1
If 2 lines intersect, then they intersect in exactly one point
Theorem 1-2
Through a line + point not in the line, there is exactly one plane
Theorem 1-3
If 2 lines intersect, then exactly one plane contains the lines
What is A.F.D?
Assume from drawing:
1) Betweeness of points
2) Betweenes of Rays
3) Straight angles
4) verticle angles
5) adjacent
(Def.) In Betweeness of Points Theorems
1) If A-B-C, then they are collinear and AB + BC = AC
2) If AB + BC = AC, then A-B-C
(Def.) Midpoint Theorems
1) If a point is a midpoint of a segment, then it divides the segment into 2 congruent segments or 2 equal lengths + collinear to the other points
2) If a point divides a segment into 2 congruent segments or 2 equal lengths, then it is a midpoint
3) If a point is a midpoint, then it divides a segment into 2 segments half as long
(Def.) Verticle Angles
If 2 angles are verticles then they are congruent/have equal measures
Congruent Segments Theorems
1) If segments are congruent, then their lengths are equal
2) If segments have equal lengths then they are congruent
Acute angle Theorems
1) If an angle is acute, then its measure is less than 90 degrees
2) If the measure of an angle is less than 90 degrees, then it is an acute angle
Right angle Theorems
1) If an angle is a right, then its measure is 90 degrees
2) If the measure of an angle is equal to 90 degrees, then it is a right angle
Obtuse angle Theorems
1) If an angle is obtuse, then its measure is greater than 90 degrees and less than 180 degrees
2) If an angle’s measure is greater than 90 degrees and less than 180 degrees, then it is obtuse
Straight angle Theorems
1) If an angle is a straight angle, then its measure is 180 degrees
2) If the measure of an angle is 180 degrees, then it is a straight angle
Betweeness of Rays Theorems
1) If Ray OA - Ray OB - Ray OC, then they are coplanar, and the m <AOB) + m <BOC = m <AOC
2) If the m <AOB) + m <BOC = m <AOC, then Ray OA - Ray OB - Ray OC
Congruent angles Theorems
1) If angles are congruent, then the measures are equal
2) If the measures of angles are equal, then they are congruent
Midray Theorems
1) If a ray is a midray of an angle, then it divides the angle into 2 congruent angles or two angles with equal measures
2) If a ray divides an angle into 2 congruent angles or two angles with equal measures, then it is a midray
3) If a ray is a midray, then it divides an angle into two angles each half as large
Complementary Angles Theorems
1) If 2 angles are complementary, then the sum of their measures is 90 degrees
2) If angles are complementary to the same angle, then they are congruent or have equal measures
3) If angles are the complement of congruent angles, then the angles are congruent
Supplementary Angles Theorems
1) If 2 angles are supplementary, then the sum of their measures is 180 degrees
2) If angles are supplementary to the same angle, then they are congruent or have equal measures
3) If angles are the supplement of congruent angles, then the angles are congruent
Vertical Angles Theorem
If 2 lines form a vertical angle, then they are congruent
Linear Pair Theorem
If two angles form a linear pair, then they are supplements