postulates and theroms and stuff Flashcards
Postulates 1 (ruler postulate)
points in a line can be matched 1:1 with real numbers. The real number that corresponds to a the coordinate of the point
Postulate 2 (Segment Addition Postulate)
If B is between A & C, then AB + BC=AC
Postulate 4 (Angle Addition Postulate)
If point B lies in the interior of <AOC, then m<AOB + m<BOC = m<AOC. If <AOC is a straight angle and B is any point not on line AC, then m<AOB + m<BOC=180
Postulate 5
A line contains at least two points; a plane contains at least three points not all in one line; space contains at least 4 points not all in one plane
Postulate 6
Through any 2 points there is exactly one line
Postulate 7
Trough any three points there is at least one (infinite) plane, nd through any three noncollinear points there is exactly one plane (only one).
Postulate 8
If 2 points are in a plane, then the line that contains the points is in that plane
Postulate 9
If 2 planes intersect, the their intersection is a line
Theorem 1
If 2 lines intersect, then they intersect in exactly one point
Theorem 2
Through a line and a point not in the line there is exactly 1 plane (similar to 3 noncollinear points)
Theorem 3
If 2 lines intersect, then exactly 1 plane contains the lines
Midpoint of a segment def
point equidistant from the endpoints of a line segment
Bisector of a segment def
a figure that passes through the midpoint of a segment
Midpoint Theorem
If M is the midpoint of line AB, then AM is ½AB and MB ½AB
Angle Bisector Theorem
If BX if the bisector of <ABC, then m<ABC=½ m<ABC and m<XBC=½ m<ABC
Vertical angles theorem
Vertical angles are congruent
2 lines are perpendicular, then theorem
If two lines are perpendicular, then they form congruent adjacent angles
converse of the perpendicular theorem
If two lines form congruent adjacent angles, then the lines are perpendicular
If the exterior sides of two adjacent acute angles are perpendicular, then what theorem
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary
if two angles are supp of congruent angles, then
If two angles are supplements of congruent/ same angles, then the two angles are congruent
if two angles are comp of congruent angles, then
if two angles are complements of congruent/ same angles, then the two angles are congruent
Scalene
no sides are congruent
Isosceles
at least 2 sides are congruent
Equilateral
all sides are congruent
Equiangular
all angles are congruent
Polygon
many angles
Convex polygon
a polygon which no line containing a side of the polygon contains a point in the interior of the polygon (simpler: not concave)
Concave polygon
a polygon which caves in (you can draw a line connecting the points between it)
Deductive reasoning
a conclusion based on accepted statements
Inductive reasoning
a conclusion based on several past observations
Corresponding Angles Converse Postulate
if 2 lines are cut by a transversal so that the corresponding angles are congruent, the lines are parallel
If two parallel lines are cut by a third plane, theorem
If two parallel lines are cut by a third plane, then the lines of intersection are parallel
Alternate Interior Angles Converse Theorem
if 2 lines are cut buy a transversal so that the alternate interior angles are congruent, then the lines are parallel
Same Side Interior Angles Converse Theorem
If 2 lines are cut by a transversal so that the same side interior angles are supplementary, then the lines are parallel
Alternate Exterior Angles Converse Theorem
If 2 lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel
If there is a line and a point not on the line, theorem
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
Two lines parallel to a third line are, theorem
Two lines parallel to a third line are parallel to each other
The sum of a triangle’s measures is what theorem
The sum of a triangle’s measures is 180
The measure of an exterior angle of a triangle equals the sum of what theorem
The measure of an exterior angle of a triangle equals the sum of the measures of the 2 remote interior angles
(n-2)180 theorem
The sum of the measure of the interior angles of a convex polygon with n sides is (n-2)180
polygon exterior 360 theorem
The sum of the measures of the exterior angles of any convex polygon is 360 degrees.
2 angles of one triangle are congruent to another 2 angles of a diff triangle, then what
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3 angles are congruent
equilateral triangle measure is what
Each angle of an equilateral triangle has a measure of 60
