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Title: Geometry Basics
Description: The basic definitions, postulates, and ideas necessary to learn geometry. This is aimed for students at a high school level, especially those entering a geometry class who would like a head start.
Description: The basic definitions, postulates, and ideas necessary to learn geometry. This is aimed for students at a high school level, especially those entering a geometry class who would like a head start.
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Basic Terms and Vocabulary
● Undefined Term - Points, lines, and planes
○ Point - names location; has no size; represented by a dot
...
Ex: ↔
○ Plane - flat surface; no thickness; extends forever; represented by a script ‘𝓡’ or
three points, not on a line
...
● Noncollinear - points that don’t lie on the same line
● Coplanar - points that lie on the same plane
● Noncoplanar - points that don’t lie on the same plane
● Segment - the part of a line consisting of two points and all points between them
...
○ Segment Bisector - a line, ray, or segment which bisects another segment
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● Ray - a part of a line that starts at an endpoint and extends forever in one direction
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● Angle - an angle is a figure formed by two rays, or sides, with a vertex
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○ Interior of an Angle - all points outside of the angle
...
○ Congruent Angles - angles that have the same measure
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○ Adjacent Angles - two angles in the same plane with a common vertex and
common side; no common interior points
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○ Complementary Angles - two angles whose measures have a sum of 90°
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○ Vertical Angles - two angles whose sides form two pairs of opposite rays; vertical
angles are two nonadjacent angles
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● Right Angle - measures 90°
● Obtuse Angle - measures greater than 90° and less than 180°
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● Coordinate - part of a set of numbers used to tell the position of a point, line, or plane
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● Length - the space from one end of something to another or from one point to another
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● Perimeter - the sum of the side lengths of the figure
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● Base - any side of a triangle
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● Diameter - a segment that passes through the center of a circle and whose endpoints are
on the circle
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● Circumference - the distance around a circle
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14…
● Hypotenuse - the longest side in a right triangle
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● Pre-image - the original figure
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● Reflection - a transformation across a line; each point and its image are the same distance
from the line of reflection
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● Translation - a transformation in which all the points of a figure move the same distance
in the same direction
...
● 1-1-2 - Through any noncollinear points there is exactly one plane containing them
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● 1-1-4 - If two lines intersect, then they intersect in exactly one point
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● 1-2-2 - If B is between A and C, then AB + BC = AC
● 1-3-2 - If S in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR
Measuring Segments
Measuring Angles
Formulas in Geometry
P = perimeter, A = area, l = length, w = width, s = side (squares because all sides are equal), a,b,
and c = sides of a triangle, h = height, C = circumference, d = diameter, r = radius
Rectangle: P = 2(l + w)
A = lw
Square: P = 4s
A = s2
Triangle = P = a + b + c
A = ½ bh
Circle: C = 𝞹d, or C = 2𝞹r
A = 𝞹r2
Midpoint and Distance
Midpoint Formula: The midpoint M of segment AB with endpoints A(x1, y1) and
B (x2,y2) is found by M = ((x1+x2/2), (y1+y2/2))
...
Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs
is equal to the square of the length of the hypotenuse
Title: Geometry Basics
Description: The basic definitions, postulates, and ideas necessary to learn geometry. This is aimed for students at a high school level, especially those entering a geometry class who would like a head start.
Description: The basic definitions, postulates, and ideas necessary to learn geometry. This is aimed for students at a high school level, especially those entering a geometry class who would like a head start.