Geometry Flashcards
1
Q
Collinear
A
Three or more points on same line
2
Q
Line
A
Defined by two distinct points and contains an infinite number of points
3
Q
Segment
A
A line bounded at both ends
4
Q
Segment Bisector
A
A line that goes through the midpoint of a segment, dividing the segment into two equal parts
5
Q
Perpendicular AKA
A
AKA Orthogonal
6
Q
Perpendicular lines
A
Meet at 90* right angles
7
Q
Perpendicular line slopes
A
Negative reciprocals
8
Q
Parallel line slopes
A
Identical slopes
9
Q
Distance Formula
A
√ (x2-x1) ^2+ (y2-y1)^2
10
Q
Slope
A
(x2-x1) / (y2-y1)
11
Q
Midpoint (between two points)
A
[(x1+x2)/2 , (y1+y2)/2]
12
Q
Angle
A
The intersection of two non-identical lines
13
Q
Angle Bisector
A
A line through the vertex that divides the angle into two equal angles (point is equidistant from sides).
14
Q
Vertex
A
The point of intersection
15
Q
Coplanar Angles
A
Lie in the same plane but are not necessarily adjacent
16
Q
Adjacent Angles
A
Share a common side
17
Q
Vertical Angles are…
A
Congruent (Angles opposite each other where two lines cross)
18
Q
Acute angle
A
Less than 90*
19
Q
Right angle
A
Equals 90*
20
Q
Obtuse angle
A
Greater than 90*
21
Q
Linear pair
A
Two angles that form a straight angle
22
Q
Congruent figures
A
Same shape and same size
23
Q
Congruent Triangles proofs
A
Side-Angle-Side, Side-Side-Side, Angle-Side-Angle, or Angle-Angle-Side
24
Q
Similar figures
A
Congruent angles and proportional sides
25
Relation
Mapping of input values to output values, or x to y
26
Reflexive relation
Can map x to itself (ie: x=x)
27
Symmetric relation
If a=b, then b=a
28
Transitive relation
a=b, b=c, therefore a=c
29
Equivalence Relation
Is reflexive, symmetric and transitive
30
Irregular/Scalene Triangle
Has NO sides that are the same length and NO angles that are the same measure
31
Scalene Triangle AKA
AKA Irregular Triangle
32
Isosceles Triangle
2 sides that are the same length and 2 angles that are the same measure
33
Equilateral Triangle
All 3 sides of equal length and all 3 angles of equal measure
34
If a² + b² = c²
Triangle is right
35
If c² (longest side) is more than a² + b²
Triangle is obtuse
36
If c² (longest side) is less than a² + b²
Triangle is acute
37
Area (of a triangle)
(1/2) base x height
38
Perimeter (of a triangle)
Sum of Sides
39
Longest side (of a triangle) is opposite which angle?
Largest Angle
40
Shortest side (of a triangle) is opposite which angle?
Smallest Angle
41
Median of a triangle
Bisects a side and passes through opposite vertex
42
Perpendicular Bisector of a triangle
Splits side, right angle to side
43
The Exterior Angle of a triangle equals...
The sum of the two remote interior angles
44
Side of a triangle must be less than...
The sum of the other two sides
45
Side of a triangle must be more than...
The difference of the other two sides
46
For 45-45-90 triangles, the hypotenuse is...
47
For 30-60-90 triangles, the length of the longer leg is ___ times the length of the shorter leg
√3
48
For 30-60-90 triangles, the hypotenuse is ___ the length of the shorter leg
2x
49
Sine = (Ratio only true for right angles)
opposite/hypotenuse
50
Cosine = (Ratio only true for right angles)
adjacent/hypotenuse
51
Tangent = (Ratio only true for right angles)
opposite/adjacent
52
Cosecant = (Ratio only true for right angles)
1/sine
53
Secant= (Ratio only true for right angles)
1/cosine
54
Cotangent = (Ratio only true for right angles)
1/tangent
55
Law of Cosines
a² = b² + c² - 2bc cosA
56
Ray
A line that begins at an initial point and extends infinitely in one direction
57
Altitude
A segment perpendicular to a side that goes through the opposite vertex (all meet at a point which might be outside the triangle)
58
Triangle midline
- A line segment from midpoint of one side to midpoint of another
- Length equals half the third side
- Midline parallel to third side
59
Geometric mean between a and b
x^2 = ab (ie: geometric mean between 4 and 9 = 6).
60
Radius (of a circle)
Distance from center to the circle
61
Diameter (of a circle)
2r distance between opposite points on the circle
62
Area (of a circle)
πr^2
63
Circumference (of a circle)
2πr or πd
64
Arc (of a circle)
a portion of the circumference
65
Minor Arc (of a circle)
less than 180\*
66
Major Arc (of a circle)
greater than 180\*
67
Chord (of a circle)
a segment with both ends on the circle
68
Secant (of a circle)
containss a chord and extends beyond the circle
69
Tangent (of a circle)
touches a circle at single point
70
Central Angle (of a circle)
An angle formed by two radii with the vertex at the center of the circle. This measure equals the arc it defines.
71
Measure of an Inscribed Angle (of a circle) is equal to...
1/2 the measure of the intercepted arc
72
Circumscribed figures (of a circle) are located on the...
outside
73
Inscribed figures (of a circle) are located on the...
inside
74
Area of a Sector is proportional to the...
central angle
75
A (sector)
pi r^2 (theta/360)
76
Quadrilateral
4 sided, sum of interior angles = 360
77
Parallelogram
A quadrilateral with 2 sets of parallel sides
78
Rectangle
A quadrilateral [and special type of parallelogram] with 4 right angles
79
Square
a rectangle with four equal sides
80
Rhombus
**A quadrilateral with all sides of equal length**
A parallelogram with four equal sides but not necessarily with 4 right angles. The diagonals are perpendicular
81
Trapezoid
has two parallel bases
82
Regular polygon
has equal sides and equal angles
83
Sum of interior angles of an n-gon =
180(n-2)
84
Apothem
The perpendicular bisector of a side that extends to the center of the polygon
85
Area of a regular polygon =
1/2 (Apothem x Perimeter)
86
Exterior Angle of a Polygon is created by....
extending one of the sides
87
The sum of the exterior angle and the adjacent angle of a polygon =
180, a linear pair
88
The sum of all exterior angles (of a polygon) in the same direction =
360
89
Midpoint between two points (a,b) and (c,d)
( [a+c]/2, [b+d]/2) think of the avg of the x coords, and avg of y coords
90
Distance between two points (a,b) and (c,d)
sq rt [(a-c)^2 + (b-d)^2]
91
Area of a trapezoid
1/2 (b1+b2) (h)
92
Complementary Angles
Two angles that add up to 90\*
93
Supplementary
Two angles that ad up to 180
94
If A=C in equation: Ax^2+Bx+Cy^2+Dy+E
circle
95
If A≠C, but same sign in equation: Ax^2+Bx+Cy^2+Dy+E
ellipse
96
If A=0 or C=0 in the equation: Ax^2+Bx+Cy^2+Dy+E
parabola
97
If A and C are opposite sign in the equation: Ax^2+Bx+Cy^2+Dy+E
hyperbola
98
directrix
a line in the plane
99
eccentricity
a measure of the shape. the closer to zero, the closer the shape is to a circle.
100
two parallel lines, two intersecting lines, or three points define a....
plane
101
two lines that are not parallel and do not meet are...
skew
102
A line that is perpendicular to a plane is perpendicular to all lines in the plane that passes through the point of...
intersection
103
A line that intersects a plane must be perpendicular to at least ___ line in the plane
one
104
Prism
has two congruent, parallel bases (a triangular prism has two parallel triangle bases, a rectangular prism has 2 rectangular bases, etc)
105
Volume of a Prism
BH (base area \* height)
106
Surface Area of a Prism
2xBase Area + Lateral Area
107
Volume of a Cylinder
πr^2 x h
108
Surface Area of a Cylinder
2 π r h + 2 π r^2
109
Volume of a Cone
110
Surface Area of a Cone
111
Slant Height of a Cone
apply pythagorean theorem
square root of altitude^2 + radius^2
112
Volume of a Pyramid
1/3 x Base area x Height
113
Surface Area of a Pyramid
B + (Perimeter x slant) / (2)
114
Volume of a Sphere
115
Surface Area of a Sphere
116
Cross Section
Made by slicing through a 3D object to produce a 2D polygon
117
The cross section of a sphere is a...
circle
118
The cross section of a triangular prism is a...
triangle or rectangle
119
The cross section of a pyramid with a square base is a...
square or triangle
120
Transformation
changes the position of a shape on a coordinate plane --- shape is moving from one place to another
121
Flip/Reflection
A shape is transposed across a line and faces the opposite direction
122
Slide/Translation
An entire shape moves in a straight path. All points on the shape move an equal distance in the exact same direction
123
Turn/Rotation
A shape moves in a circular path around an axis point
124
Isometry
Transformation in two or three dimensions that preserves distance, shape and size
125
Dilation
Transformation that retains shape but changes size. Resulting image is in proportion (or scale) to original
126
Similar shape
congruent angles and proportional sides
127
If the side of a square is doubled, the area increases by a factor of...
^2
128
If the side of a cube is doubled, the volume increases by a factor of...
^3
129
If the radius of a circle is doubled, the circumference is doubled, and the area increases by a factor of...
^2
130
pentagon
5 sides
131
hexagon
6 sides
132
octagon
8 sides
133
heptagon
7 sides
134
nonagon
9 sides
135
decagon
10 sides
136
trapezoid
a convex quadrilateral with at least one pair of parallel sides
137
Centroid (of a circle) how to find...
The point of concurrency for the medians of a triangle (bisecting each line segment). Centroid is the point of balance for any triangle.
138
Incenter (of a circle) how to find...
The point of concurrency of the angle bisectors
139
Circumcenter (of a circle) how to find...
The point of concurrency of the perpendicular bisectors
140
Conversion formulas to convert from polar coordinates to rectangular coordinates.
x = (r)cosθ and y = (r)sinθ
141
Outside Angles Theorem (tangents or secants of circles)
1/2 (major arc - minor arc) = angle of the outside angle
142
Distance from a point to a line formula (h, k) and Ax + By + C = 0
|Ah + Bk + C| over SqRt A^2 + B^2
143
Interior angles of a regular polygon
180(n-2)
144
Exterior angles of a regular polygon
360/n
145
Golden ratio
Approx 1.618 : 1
146
Angle Bisector of a triangle
- Splits an angle and extends to a side
- Meeting point is equidistant from the sides
147
Altitude of a Triangle
- Segment perpendicular to a side that goes through opposite vertex
- All point meet, which might be outside the triangle
148
