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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
01:44
Relationships Within Triangles
Altitude Example
Altitude or height is defined based on the context in which it is used (as a height above sea level, or as height above the ground, or as height above the ground or sea level). As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term "elevation" is often preferred for this usage.
Kurt Kleinberg
06:25
Relationships Within Triangles
Altitudes
In mathematics, an altitude is the perpendicular distance from a geometric figure to its line of intersection with a horizontal plane. The word altitude comes from the Latin word "altitudo", meaning "height".
Kurt Kleinberg
04:31
Relationships Within Triangles
Angle Bisector Examples
In mathematics, an angle bisector of a polygon is a line segment dividing the angle of the polygon in two equal angles. It is a special case of the line bisector of a segment.
Kurt Kleinberg
07:13
Relationships Within Triangles
Angle Bisectors and Incenters
In geometry, the bisector of an angle of a triangle is a line segment that bisects the angle, that is, divides it into two equal angles. In a triangle, the bisector of an angle is the line through the vertex that divides the opposite side into segments with lengths proportional to the adjacent sides. In a circle, the bisector of an angle is a chord that passes through the center of the circle and divides the angle in half. The incenter of a triangle is the center of its incircle, the circle passing through all three vertices of the triangle.
Kurt Kleinberg
03:49
Relationships Within Triangles
Identifying Congruent Triangles Quick
In geometry, two triangles are congruent if they have the same shape and size. The word is occasionally used to refer to all similar triangles. Two triangles are similar if both pairs of corresponding sides are in the same ratio, and the included angles also match.
Kurt Kleinberg
07:46
Relationships Within Triangles
Intro to Congruent Triangles
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ? ABC. In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (the triangle's plane). This article is about triangles in Euclidean geometry, and in other geometries.
Kurt Kleinberg
03:30
Relationships Within Triangles
Isosceles and Equilateral Triangles
An isosceles triangle is a triangle in which at least two sides have the same length. An equilateral triangle is a triangle in which all three sides have the same length.
Kurt Kleinberg
03:50
Relationships Within Triangles
Isoscelese and Equilateral Examples
In geometry, an isosceles triangle is a triangle in which two sides have equal lengths. The term isosceles triangle is also used to refer to any triangle that has at least two congruent sides, regardless of the lengths of the other two sides. The base angles of an isosceles triangle are also equal. An equilateral triangle is a special case of an isosceles triangle with all three sides equal in length, and equiangular triangle is a special case of isosceles triangle with all three angles equal.
Kurt Kleinberg
08:18
Relationships Within Triangles
Medians Centroid and Examples
In mathematics, the median is a measure of the "middle" value of a data set. The median is a commonly used measure of the properties of a set in statistics and probability theory. The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest, and finding the middle one. For example, the median of the list [3, 4, 6, 7, 8, 9] is 6. If there is an even number of elements, then there is no single middle value. In this case, one may take the mean of the two middle values. For example, the median of the list [3, 4, 4, 6, 7, 8, 9] is (4+6)/2 = 4.5.
Kurt Kleinberg
10:43
Relationships Within Triangles
Proving Triangles Congruent Cont
In mathematics, two triangles are congruent if they have the same shape and size. More formally, two triangles are congruent if both of the following statements are true: 1) the triangles have two corresponding angles, and 2) the corresponding sides have the same length. The first statement says that the triangles share the same angles. The second statement says that the triangles share the same sides. The corresponding sides are the pairs of sides that are connected to the same vertex. The corresponding angles are the pairs of angles that are opposite the same side.
Kurt Kleinberg
12:14
Relationships Within Triangles
Proving Triangles Congruent Proofs
In geometry, two triangles are congruent if they have the same size and shape, or if one can be transformed into the other by a combination of rotations, reflections, and translations.
Kurt Kleinberg
08:27
Relationships Within Triangles
Similar Triangle Examples with Algebra
In geometry, similarity is a relationship between two geometric figures. The precise definition depends on the type of figures being considered.
Kurt Kleinberg
07:47
Relationships Within Triangles
Similar Triangles
In geometry, similarity is a relationship between two geometric figures. The similarity transformation is a rigid transformation, i.e. a transformation that preserves the lengths of all vectors (or, in other words, the areas of all figures).
Kurt Kleinberg
11:36
Relationships Within Triangles
Similar Triangles Proofs
In geometry, two triangles are said to be similar if they have the same angles, and the corresponding sides are in proportion. Two triangles are similar if their corresponding angles are equal.
Kurt Kleinberg
06:28
Relationships Within Triangles
Slope Formalized
In mathematics, a slope or gradient of a line is a number that describes both the direction and the steepness of the line. The direction of a line is increasing, decreasing, horizontal, or vertical. The steepness is how much the line changes direction over a given distance. The slope can be expressed in several ways: as an angle made with the horizontal, as a ratio of distances, as a fraction, as a percentage, or as a vector.
Kurt Kleinberg
06:00
Relationships Within Triangles
Triangle Classifications
In mathematics, triangle classification is the classification of triangles into categories based on their properties. The triangle classification problem was first posed by Hilbert in 1902 and solved in the negative in 1983 by Robertson and Seymour. Classification of triangles is an important problem in computer vision and image processing, and is used for example in image analysis and automatic optical inspection.
Kurt Kleinberg
10:41
Relationships Within Triangles
Triangle Congruence Theorems
In geometry, two triangles are congruent if they have the same shape and size. More precisely, two triangles are congruent if one can be moved so that it exactly covers the other, with one side of the one matching up with the corresponding side of the other. The word congruent is derived from the Latin congruus, meaning "agreeing in length" or "of the same length".
Kurt Kleinberg
04:24
Relationships Within Triangles
Triangle Inequality Theorem Algebraic Example
In mathematics, the triangle inequality states that for any triangle "ABC", the length of any side must be less than the sum of the other two sides or the other two sides must be greater than the length of the given side. The triangle inequality is a basic property of Euclidean geometry, and is used to prove theorems such as the Pythagorean theorem and the law of cosines.
Kurt Kleinberg
06:27
Relationships Within Triangles
Triangle Inequality Theorem and Examples
In mathematics, the triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side, if the triangle is not isosceles. The inequality is a consequence of the fact that the two shorter sides of a triangle must be adjacent (that is, one side of the triangle must be between the other two sides).
Kurt Kleinberg