Midterm Review Flashcards
What are the undefined terms in geometry
Point, Line, Plane
Segment Def
A figure bounded by two distinct points on a line
Ray Def
a sequence of points with one endpoint or point of origin extending infinitely in one direction
Opposite Ray Def
Two rays with the same endpoint that extend in opposite directions
Congruence Def
The quality of having the exact same size and shape as another figure
Betweenness def
The quality of being between two other points on a line
Midpoint Def
A point that divides a segment into two congruent segments
Segment Bisector Def
A line that divides a segment into two congruent segments
Distance Def
The length between two distinct points
Angles Def
A figure formed by two rays sharing a common endpoint
Angle Bisector Def
A ray that divides an angle into two congruent angles
Collinear Def
The quality of being on the same line as another point
Segment Addition Postulate
The length of two segments may be added together to form one greater length
Angle Addition Postulate
The measure of two angles may be added together to form an angle of greater measure
Linear Pair Definition
A pair of adjacent angles whos non common sides are formed by opposite rays
Midpoint Formula
((x1 + x2)/2, (y1 + y2)/2)
Distance formula
d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}
Symetrical Property of Equality/Congruence
If a = B, B = A
Linear Pair Theorem
If two angles form a linear pair, they are supplementary
congruent Supplements Theorem
If <A and <B is a supplement of <C, <A=~<B
Right Angle Congruence Theorem
All right <s are equal
Congruent complements theorem
If <A and <B are complement of <C, <A=~<B
Common Segments Theorem
If two collinear segments share a common segment and the non-overlapping parts are congruent, then the two larger segments are congruent.
A—B—C—D
If AB = CD, AC=BD
Vertical Angles Theorem
Vertical angles are congruent
Congruent Sup. Are Right
Congruent supplements are always right
Perpendicular Def
At an angle of 90°/Right angle to a given line, plane, or surface.
Skew Line
Neither parallel nor intersecting
PCA
If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent
PAI
Paralell Alternate Exterior is congrent
PAE
Parallel alternate interior is congreunt
PSSIS
Parallel Same Side Interior is supplementary
CAP
If each pair of corresponding angles are congruent, two parallel lines are cut by a transversal
AIP
If alternate interior angles are congruent, the lines they cut are paralell
SSISP
If Same Side Interior angles are supplementary, the lines they cut are paralel
Perpendicular transversal theorems
if there are two parallel lines in the same plane and there’s a line perpendicular to one of them, then it’s also perpendicular to the other one.
Lines perpendicualr to the transversal theorem
If two lines are perpendicular to the same transversal, then the two lines are parallel to each other.
Triangle Sum Theorem
the sum of the three interior angles of any triangle is always 180 degrees.
HL
If the hypoteneus and leg of two right triangles are congruent, then the triangle as a whole is congruent
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
BAT
Base angles are congruent in isosceles triangles
CBAT
If base angles are congruent a triangle is isosceles
Perpendicular Bisector Theorem
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Angle Bisector Theorem
when an angle in a triangle is split into two equal angles, it divides the opposite side into two parts.
Centroid Theorem
the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
Midsegment Theorem
the midsegment between any two sides of a triangle is parallel to and half the length of the third side.
Centroid
The point of concurrency for the medians
Incenter
The point of concurrency of the angle bisectors
Orthocenter
The point of concurrency for altitudes
Circumcenter
The point of concurrency for perpendicular bisectors
Median Def
Vertex to opposite sides midpoint
Altitude def
Vertex to opposite side perpendicular to opposite side
30-60-90
S = Shortest, L = Longer, H = Hypotenuse:
L=Sx(sqr root 3), H = 2S
45-45-90
H=L(sqr root of 2)
Hinge Theorem
If two triangles have two congruent sides (sides of equal length), then the triangle with the larger angle between those sides will have a longer third side.
Tabula Rasa
