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Geometry
Geometry Camp
Geometry
12 topics
101 lectures
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Camp Curriculum
Circles
17 videos
Parallel and Perpendicular lines
14 videos
Deductive Reasoning
1 videos
Non Rigid Transformations (Dilations)
2 videos
Polygons
6 videos
Geometry Basics
3 videos
Properties of Quadrilaterals
5 videos
Right Triangles
13 videos
Rigid Motions (Isometries)
6 videos
Volume
10 videos
Terminology
5 videos
Relationships Within Triangles
19 videos
Lectures
03:38
Parallel and Perpendicular lines
Distance Formula Derivation
In mathematics, a distance or metric is a function that defines a distance between each pair of elements of a set. A set is a collection of elements, and the distance between two elements a and b of this set is defined as the minimum number of steps needed to get from a to b, where the steps are taken along the edges connecting a and b. In other words, the distance is the minimum number of edges that have to be passed from a to b. The distance may be thought of as the length of the smallest path connecting the two points.
Kurt Kleinberg
05:16
Parallel and Perpendicular lines
Distance Formula Examples
In mathematics, a distance matrix is a matrix whose rows and columns are the distances between pairs of the set of points from which the matrix is constructed. The entries of the matrix are non-negative and sum to the total distance between the points.
Kurt Kleinberg
20:13
Parallel and Perpendicular lines
Equations of Lines
In mathematics, a line is a straight line segment with zero curvature, meaning that it is a line in the Euclidean plane with no inflection points. The concept of a line is one of the most fundamental concepts in geometry, building a bridge between Euclidean geometry and algebra. In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For example, in analytic geometry a line may be defined as a set of points satisfying a linear equation, while in synthetic geometry it is described as a set of points satisfying a geometric theorem.
Kurt Kleinberg
08:43
Parallel and Perpendicular lines
Equations of Lines Examples
In mathematics, the equations of a line are parametric equations, usually written in the form (x?x_1)/cos? ? = (y?y _1)/sin? =r, where r is the parameter which is distance between the point (x,y) and (x_1,y_1).
Kurt Kleinberg
01:52
Parallel and Perpendicular lines
Midpoint Formula Derivation
In mathematics, the midpoint formula is a formula for the coordinates of the midpoint of a line segment between two points with Cartesian coordinates (x1, y1) and (x2, y2).
Kurt Kleinberg
05:35
Parallel and Perpendicular lines
Midpoint Formula Examples
In geometry, the midpoint formula is used to find the coordinates of the midpoint of a line segment between two points in the Euclidean plane.
Kurt Kleinberg
09:47
Parallel and Perpendicular lines
Parallel and Perpendicular Lines
A line is a one-dimensional linear object with no thickness, length, width, or breadth. A line is either straight or curved.
Kurt Kleinberg
14:47
Parallel and Perpendicular lines
Parallel and Perpendicular examples
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.
Kurt Kleinberg
10:19
Parallel and Perpendicular lines
Partitioned Line Segments
In mathematics, partitioning a line segment is a way of dividing a line segment into two, three, or more line segments of equal length. The partitions of a line segment are the collection of all the ways of dividing it. For example, one can partition a line segment into two equal pieces by dividing it at its midpoint or by dividing it into three equal pieces by dividing it at its midpoint twice.
Kurt Kleinberg
08:55
Parallel and Perpendicular lines
Perpendicualr Bisectors
In mathematics, the perpendicular bisector of a segment is a line that passes through the midpoint of the segment and is perpendicular to it. The perpendicular bisector of a ray is a line that passes through the midpoint of the ray and is perpendicular to it.
Kurt Kleinberg
02:10
Parallel and Perpendicular lines
Perpendicular Bisector examples with algebra
In geometry, a perpendicular line is a line perpendicular to another line. The word "perpendicular" comes from the Latin word "perpendiculum", meaning "a rod to hang from". The perpendicular is the line that is perpendicular to the plane of the other line. The definition of perpendicular lines is based on two equivalent definitions: A line is perpendicular to another line if the two lines intersect and no point on the second line lies on the first line. A line is perpendicular to another line if the two lines are not parallel and a point on the second line lies on the first line. The first definition follows from the second, since the angle between two lines is 90 degrees.
Kurt Kleinberg
06:24
Parallel and Perpendicular lines
partioned Segments Examples
In mathematics, a partition of a set "S" is a collection of non-empty subsets of "S" such that every element is contained in exactly one of the subsets. The partition (or disjoint-set data structure) problem is the problem of finding a partition of a given set "S" into a minimum number of non-empty subsets. The problem was first formulated in 1936 by Frank Rubin and is also known as the "Rubin partition problem".
Kurt Kleinberg
10:22
Parallel and Perpendicular lines
Applications of Parallel Lines
Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.
Kurt Kleinberg
09:54
Parallel and Perpendicular lines
Definition of Parallel Lines and Relationships
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.
Kurt Kleinberg