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Foundations of Geometry
What is geometry? Some of the world's greatest and oldest civilizations each developed geometry independently. Let's look at their contributions and define geometry.
5 minutes
All levels
English
Inductive reasoning is used to form hypotheses, while deductive reasoning can be helpful in solving geometric proofs. Want to see the video?
5 minutes
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An axiomatic system is a collection of axioms, or statements about undefined terms. You can build proofs and theorems from axioms. Want to see the video?
5 minutes
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In geometry, three undefined terms are the underpinnings of Euclidean geometry: point, line, and plane. Want to see the video?
5 minutes
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Geometric figures are powerful pieces in geometry that are undefined and form the bedrock foundation of classical geometry. Want to see the video?
5 minutes
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Skew lines are lines that are in different planes, they are never parallel, and they never intersect. Want to watch the video on Skew Lines and learn more?
5 minutes
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A horizontal line is a line that neither rises nor falls; it has no slope at all. Learn how to plot a horizontal line on a graph, and find it's slope in this video.
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Parallel lines are two or more lines that are the same distance apart, never merging and never diverging. Learn symbols, see examples, graph and construct parallel lines in this video!
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What are parallel sides? Learn the definition of parallel sides and how they apply to parallel shapes with parallel sides. Check out these examples and video!
5 minutes
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Learn how to construct and draw a perpendicular line through a point on the line. Construct perpendicular lines using examples and prove lines are perpendicular.
5 minutes
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A line graph uses a grid of intersecting perpendicular lines formed by an x-axis and a y-axis, over which you show changes over time, using a line. Want to see the video?
5 minutes
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Learn the definition of a line segment, how to measure line segments on a Cartesian or coordinate plane, and use the distance formula. Want to see the video?
5 minutes
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Learn the definition of a ray in geometry. Learn how to draw a ray in math using ray symbols and examples. Want to see the video?
5 minutes
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All right, let's get one thing straight… a straight line, that is. What could be simpler in geometry than the elegant, sparse, straight line? Watch the video >
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In this free video lesson: learn and define the coordinate plane and terms used in coordinate planes, including axis, coordinate pair, origin, scale, quadrant, and intercept.
6 minutes
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A Cartesian coordinate system specifies each point in a plane by a set of numerical coordinates. Learn about the Cartesian coordinate system in this free lesson.
6 minutes
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Learn the definition of geometric probability, and use the formula for geometric probability to calculate the likelihood of an outcome involving flat shapes. Want to see the video?
5 minutes
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A cardioid is a mathematically generated shape resembling a heart or half an apple. Constructing a cardioid on a polar graph is done using equations. Want to see?
5 minutes
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Mathematical Logic
Learn the definition of the law of syllogism, review clear examples of syllogisms, and apply the law of syllogism to generate valid conclusions from valid premises.
5 minutes
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One of the most powerful types of proof in mathematics is proof by contradiction. Our examples show it can be used to prove any statement, in several fields of mathematics.
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Mathematical induction is a method of proof that is used in mathematics and logic. Learn what mathematical induction is and the 3 steps in a mathematical induction.
7 minutes
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A two-column proof uses a table to present a logical argument and assigns each column to do one job to take a reader from premise to conclusion. Want to learn?
7 minutes
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Mathematical and logical statements are joined with connectors; conjunctions and disjunctions are two types of logical connectors. Learn with easy examples >
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Four testable types of logical statements are converse, inverse, contrapositive and counterexample statements. Learn step-by-step with these examples and video.
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There are 3 easy steps on how to do an Indirect Proof. Follow easy examples step-by-step. Learn the definition, and how to write Indirect Proofs. Want to learn?
5 minutes
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Define tautology in discrete math and learn how to use logic symbols and truth tables in tautology examples. Want to see the video?
6 minutes
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Antisymmetric relation is a concept of set theory that builds upon both symmetric and asymmetric relation. Watch the video with antisymmetric relation examples.
6 minutes
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What is a biconditional statement? Learn the definition, view biconditional statement examples, and learn how to write a biconditional statement step-by-step.
6 minutes
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Introduction to Geometric Figures
What is geometric construction? Geometric construction allows you to construct lines, angles, and polygons with a compass and straightedge using these methods.
5 minutes
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Learn what similar figures are and their definition. Learn how to solve similar figures using ratios and proportions and review similar triangles with examples.
5 minutes
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Learn the types of angles and angle relationships between them. Learn exterior, interior, congruent, adjacent, vertical, corresponding, and alternating angles.
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Learn how to construct 30°, 60°, 90° and 120° degree angles in this video. The construction of angles is easy with only a compass, a pencil, and a straightedge.
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Learn how to construct or draw an equilateral triangle. Equilateral triangles are easily constructed with a drawing compass, straightedge, and pencil.
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Learn how to construct an angle bisector with only a drawing compass, pencil, and straightedge. Want to watch this angle bisector construction video?
5 minutes
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Learn how to graph points on a coordinate plane. In this lesson, we will plot points on the coordinate graph. Want to see the video?
5 minutes
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Learn the definition of collinear points and the meaning in geometry using these real-life examples and watching the free video.
5 minutes
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Surface Area
Learn how to find the surface area of a rectangular prism with this formula. Easily calculate surface area step by step with examples. Want to watch the video?
5 minutes
All levels
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Learn how to find the surface area of a cylinder using the surface area of a cylinder formula. Also, learn the lateral surface area formula in the free video.
5 minutes
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Learn how to find the surface area of a pyramid with surface area formulas. Learn to find lateral area and surface area for square and rectangular pyramids.
5 minutes
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Properties of Triangles
Learn how to find the area of a triangle using this formula. Easy step-by-step examples for finding area. Want to see the video?
5 minutes
All levels
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Learn how to find the area of a right triangle using this formula. Easy step-by-step examples for finding the area. Want to see the video?
5 minutes
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Learn how to find the perimeter of a triangle using this formula. Easy step-by-step examples for finding the perimeter of any triangle. Want to see the video?
5 minutes
All levels
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Learn how to find the perimeter of a rectangle using this formula. Easy step-by-step examples for finding the perimeter of any rectangle. Want to see the video?
5 minutes
All levels
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Learn what a triangle is, the properties of triangles, and examples of the types of triangles. We go over sides, angles, altitude, and parts of a triangle in this video.
7 minutes
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Learn how to classify triangles by their angles & sides. In total, we have seven ways to describe and classify triangles. Want to check out the video?
5 minutes
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Define and identify interior angles and exterior angles of triangles. Use properties of angles and triangles to calculate unknown interior angles and exterior angles.
5 minutes
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The median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it. Every triangle has exactly three medians. Want to see?
5 minutes
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Learn the formula for how to find the altitude of a triangle and calculate altitudes for equilateral, isosceles, and right triangles. Want to see the video?
5 minutes
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Learn the point of concurrency definition, and the four different kinds of points of concurrency, which are the centroid, circumcenter, incenter and the orthocenter.
4 minutes
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Learn how to find the height of a triangle using two different formulas. (The Pythagorean Theorem or the area formula). Want to see the video and learn how?
7 minutes
All levels
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Learn the definition of a hypotenuse, and use the hypotenuse formula to find the length of an unknown side, or the measure of an unknown angle. Want to see the video?
5 minutes
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An included angle is the angle between two line segments or rays. For any triangle, its three interior angles are each included between two sides. Want to see the video?
5 minutes
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Learn the Interior Angle Formula for polygons, apply the formula to find the sum of the interior angles of a polygon, and use it to find an unknown interior angle.
5 minutes
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A midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments. Want to see?
5 minutes
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Learn the definition of a segment bisector and identify the various forms of segment bisectors, including line segments, lines, rays and points. Want to see the video?
7 minutes
All levels
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Learn what a centroid is and learn how the find the centroid of a triangle in this free lesson. Want to see the video?
6 minutes
All levels
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Learn how to find the orthocenter of a triangle in this free geometry video. Learn the four steps needed to find the coordinate points of a triangle's orthocenter.
6 minutes
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The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Want to see the video?
5 minutes
All levels
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Triangles, Theorems and Proofs
Similar triangles are triangles with the same shape but different side measurements. Learn how to prove triangles similar with these theorems. Want to check it out?
5 minutes
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Testing to see if triangles are congruent involves three postulates, the Angle Side Angle (ASA), Side Angle Side (SAS), and Side Side Side (SSS). Want to check it out?
5 minutes
All levels
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Conditional statements set up conditions that could be true or false. Let's go over examples of conditional statements, and how to produce the converse of a conditional statement. Want to see?
5 minutes
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Learn the three similarity transformations in geometry (rotation, reflection, and translation). Apply the three transformations to compare polygons. Want to check it out?
5 minutes
All levels
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Learn the Angle Angle Side (AAS) Theorem, relate the AAS Theorem to the ASA Postulate, and learn how AAS helps to determine congruence in triangles. Want to check it out?
5 minutes
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Learn the Hypotenuse Angle (HA) Theorem, demonstrate the HA Theorem's connection to the ASA Theorem, and mathematically prove the HA Theorem. Want to check it out?
5 minutes
All levels
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Learn the Hypotenuse Leg (HL) Theorem, use the HL Theorem to prove congruence in right triangles, and learn that corresponding parts of congruent triangles are congruent. Want to see?
5 minutes
All levels
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Learn the perpendicular bisector theorem, how to prove the perpendicular bisector theorem, and the converse of the perpendicular bisector theorem. Want to check it out?
5 minutes
All levels
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Learn the two theorems (LA & LL Theorems) to prove the congruency of right triangles. Then, we'll apply the right angle congruence theorem to examples. Want to check it out?
5 minutes
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Learn how to prove congruent isosceles triangles using the Isosceles Triangles Theorem. Also, prove the converse of the Isosceles Triangles Theorem in these examples. Want to see?
5 minutes
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Learn the definition of Alternate Exterior Angles, and use the Theorem to prove alternate exterior angles are congruent with these examples. Want to see the video?
5 minutes
All levels
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Learn the definition of Alternate Interior Angles, and use the Theorem to find angles in parallel lines crossed by a transversal in these examples. Want to see?
5 minutes
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Learn what the terms angle of elevation and angle of depression mean. See examples from everyday life of the angle of depression and the angle of elevation in this video.
5 minutes
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Learn the vertical angles definition and vertical angles theorem. Determine if vertical angles are congruent, adjacent, supplementary, or complementary angles.
5 minutes
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The Midpoint Theorem states that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
5 minutes
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Learn and apply the perpendicular bisector definition, and learn how to construct a perpendicular bisector using simple tools. Want to see the video?
8 minutes
All levels
English
Learn what a square matrix is, identify the elements of matrices, and perform operations of addition, subtraction, and multiplication using matrices.
5 minutes
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Parallel Lines & Polygons
Learn about Parallel and Perpendicular Lines and how to use line equations to plot the slope. Want to see these examples and learn step by step?
4 minutes
All levels
English
In this lesson we will define a transversal in parallel lines, classify transversal angles, and identify angles created by a transversal in parallel lines.
4 minutes
All levels
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In this video lesson, we will show you how to prove lines are parallel using a transversal and the angles it creates. Want to watch the free video?
6 minutes
All levels
English
Constructing parallel lines is one skill you will need to know. Learn how to draw parallel lines using only a pencil, straightedge and compass (no measuring!).
6 minutes
All levels
English
In this lesson we will define and apply the Parallel Postulate of Euclid. Learn how to draw and test the Parallel Postulate with these examples. Want to see?
6 minutes
All levels
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Learn all the different types of polygons. Distinguish between regular and irregular polygons, simple and complex polygons, and concave and convex polygons.
6 minutes
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Learn what a regular polygon is, state the identifying properties and definition of regular polygons, and name examples of regular polygons. Want to see?
7 minutes
All levels
English
Learn the Diagonal Formula for calculating the number of diagonals of a polygon. The diagonal formula works on: squares, rectangles, and cubes. Want to see?
6 minutes
All levels
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With this formula we will learn how to find the perimeter of any polygon. Then, we will apply knowledge of regular polygons to calculate perimeter quickly.
6 minutes
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With this formula we will learn how to find the area of any regular polygon. Then, we will define and apply the apothem of any regular polygon. Want to see?
6 minutes
All levels
English
In this lessons learn all about area and perimeter with these nifty formulas. Find the area and perimeter of circles, rectangles, squares and more. Want to see?
5 minutes
All levels
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With this formula we will learn how to find the angle of a triangle with these examples. Easily calculate the missing measurement of any angle of a triangle.
6 minutes
All levels
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With this formula we will learn how to find the sum of exterior and interior angles of a regular polygon. Want to check out the video and lesson?
6 minutes
All levels
English
A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. Want to check out all the decagon shapes in this video?
6 minutes
All levels
English
Similar Polygons
Learn the definition of ratios and proportions, and learn the relationship between ratios and proportions. Want to check out the video and lesson?
6 minutes
All levels
English
Learn the definition of geometric mean and how to find it using the geometric mean formula. Want to check out the video and lesson?
6 minutes
All levels
English
Learn the definition of an Angle Bisector and learn the Angle Bisector Theorem with step by step examples. Want to check out the video and lesson?
6 minutes
All levels
English
Learn how to solve proportions. Easy step-by-step examples to solving proportions. Want to check out the video and lesson?
6 minutes
All levels
English
Learn how to use the transitive property to prove that size is the only difference between similar triangles. Want to check out the video and lesson?
6 minutes
All levels
English
Learn and apply the Triangle Proportionality Theorem to common situations encountered in daily life. Want to check out the video and lesson?
6 minutes
All levels
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Learn what a right triangle is, the definition of a right triangle, and the right triangle formula in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn the Pythagorean Theorem, and apply the Pythagorean Theorem Formula to calculate the length of one side of a right triangle. Want to check out the video and lesson?
6 minutes
All levels
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Learn the converse of the Pythagorean Theorem. Step by step video with examples. Want to check out the video and lesson?
6 minutes
All levels
English
Learn how to use the Pythagorean Theorem to find Pythagorean triples. Step by step video with examples and list. Want to check out the video and lesson?
6 minutes
All levels
English
Learn what a polygon is, the definition of a polygon, and the shapes that make up the polygon family in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Quadrilaterals
Learn what a quadrilateral is, the definition of a quadrilateral, the shapes, and the properties of quadrilaterals in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn what a parallelogram is, the definition of a parallelogram, and the properties of a parallelogram in this lesson. Want to check out the video and lesson?
6 minutes
All levels
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Learn the forumla for how to find the area of a parallelogram. Step-by-step video lesson. Want to check out the video and formula?
6 minutes
All levels
English
Learn what a rhombus is, identify the five features of a rhombus, and apply three different formulas for finding the area of a rhombus.
6 minutes
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Learn the forumla for how to find the area of a rhombus. Step-by-step video lesson. Want to check out the video and formula?
6 minutes
All levels
English
Learn what kites are in geometry, the definition of a kite, and the properties of kites in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn what a rectangle is, the definition of a rectangle, and the properties of a rectangle in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn the forumla for how to find the area of a rectangle. Step-by-step video lesson. Want to check out the video and formula?
6 minutes
All levels
English
Learn what a square is, the definition of a square, and the properties of a square in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn what a trapezoid is, the definition of a trapezoid, and the properties of a trapezoid in this lesson. Want to check out the video and lesson?
6 minutes
All levels
English
Learn the forumla for how to find the area of a trapezoid. Step-by-step video lesson. Want to check out the video and formula?
6 minutes
All levels
English
Learn and apply Heron's Formula for finding the area of a triangle in this lesson. Want to check out the video?
6 minutes
All levels
English
What is an irregular quadrilateral? Irregular quadrilaterals are: rectangle, trapezoid, parallelogram, kite, and rhombus. Learn the definition and area here.
6 minutes
All levels
English
Circles and Circular Arcs
Learn the relationships and formulas for radius, diameter, and circumference of a circle. Want to learn how to find the circumference of a circle?
6 minutes
All levels
English
Learn the definition of an inscribed angle and a central angle of a circle, and apply the Inscribed Angle Theorem in this lesson. Want to see the video?
5 minutes
All levels
English
Learn how to find the Arc Length of a circle using the Arc Length Formula in both degrees and radians. Learn step-by-step with these examples. Want to see?
6 minutes
All levels
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Learn how to find the Arc Measure of a circle using the Arc Measure Formula in both degrees and radians. Learn step-by-step with these examples. Want to see?
6 minutes
All levels
English
A tangent to a circle is a line that intersects a circle at exactly one point. The tangent must be at a right angle to a radius that intersects that same point.
6 minutes
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Learn how to find the area of a circle using the formula for radius, diameter, and circumference. Easily calculate the area with these step-by-step examples.
6 minutes
All levels
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Learn how to find the area of a sector of a circle using the area of a sector formulas. Complete examples using arc length, central angle, and sector radians.
6 minutes
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Learn how to find the equation of a circle with easy examples. We cover the Standard Form Equation of a circle as well as the General Form Equation of a circle.
6 minutes
All levels
English
Here are the steps on how to complete the square. 7 steps are all you need to complete the square in any quadratic equation. Want to learn step-by-step?
6 minutes
All levels
English
Learn how to graph a circle in 4 easy steps with these circle graph equations. Want to watch the video and learn to plot a circle on a graph step-by-step?
6 minutes
All levels
English
Geometric Solids
Learn the definition, history, uses, and see images of the 5 Platonic Solids. The five solids are a tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
6 minutes
All levels
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In geometry, a polyhedron is a three-dimensional shape with straight edges and sharp corners or vertices. Every face must be composed of polygons. Want to learn?
6 minutes
All levels
English
Analytic Geometry
The distance formula is used to find the distance between two points. Use this Distance Formula Calculator to easy find your answer, and learn step by step how to solve.
5 minutes
All levels
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The Midpoint Formula is applied when one is required to find the center point between two defined points. Learn how to find the midpoint with this equation.
5 minutes
All levels
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Learn how to find the distance between two parallel planes using the point-plane distance formula with these 4 easy steps. Want to see the video?
6 minutes
All levels
English
Geometry Help (with Videos & Lessons)
Get geometry help for free. Learn transformations, congruence, similarity, theorems, formulas, and more. Want to check out the videos and lessons?
Get started: What is a Quadrilateral?
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