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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 All levels English
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 All levels English
In geometry, three undefined terms are the underpinnings of Euclidean geometry: point, line, and plane. Want to see the video?
5 minutes All levels English
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 All levels English
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 All levels English
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.
5 minutes All levels English
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!
5 minutes All levels English
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 All levels English
Learn the definition of congruence and similarity in math. We will cover the properties and congruent examples for similar shapes. Want to see?
5 minutes All levels English
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 All levels English
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 All levels English
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 All levels English
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 All levels English
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 >
5 minutes All levels English
What does perimeter mean in math? The definition of perimeter in math is the distance around a two-dimensional or even a 3D object. Want to learn?
5 minutes All levels English
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 All levels English
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 All levels English
What is the X-coordinate? The x-coordinate tells you how far along the x-axis to move to your location. Plot a point on a graph with one Y and one X-coordinate.
6 minutes All levels English
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 All levels English
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 All levels English

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 All levels English
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.
5 minutes All levels English
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 All levels English
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 All levels English
Mathematical and logical statements are joined with connectors; conjunctions and disjunctions are two types of logical connectors. Learn with easy examples >
5 minutes All levels English
Four testable types of logical statements are converse, inverse, contrapositive and counterexample statements. Learn step-by-step with these examples and video.
5 minutes All levels English
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 All levels English
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 All levels English
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 All levels English
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 All levels English

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 All levels English
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 All levels English
Congruent figures in geometry are identical in shape and size. Learn the definition, view examples, and check out different shapes. Want to see?
5 minutes All levels English
Learn the types of angles and angle relationships between them. Learn exterior, interior, congruent, adjacent, vertical, corresponding, and alternating angles.
5 minutes All levels English
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.
5 minutes All levels English
Learn how to construct or draw an equilateral triangle. Equilateral triangles are easily constructed with a drawing compass, straightedge, and pencil.
5 minutes All levels English
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 All levels English
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 All levels English
Learn the definition of collinear points and the meaning in geometry using these real-life examples and watching the free video.
5 minutes All levels English
What are adjacent angles? The definition of adjacent angles are two angles sharing a common side and vertex and exist as pairs. Want to see these examples?
5 minutes All levels English
What are supplementary angles? Learn the definition of supplementary angles, view examples of two angles that are supplementary, and how to find them.
5 minutes All levels English
Angle pairs always appear as two angles working together to display an interesting property. We will look at nine different types of angle pairs.
5 minutes All levels English

Area, Surface Area & Volume

What is area in math? In geometry, the area is the amount of space a flat shape -- figures like a polygon, circle or ellipse -- takes up on a plane.
5 minutes All levels English
What is surface area? Surface area of 3D solids is the measured area, in square units, of all the surfaces of an object. Want to see our formulas and examples?
5 minutes All levels English
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 English
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 All levels English
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 All levels English

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 English
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 All levels English
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 English
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 English
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 All levels English
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 All levels English
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 All levels English
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 All levels English
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 All levels English
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 All levels English
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 English
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 All levels English
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 All levels English
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 All levels English
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 All levels English
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 English
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 English
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 All levels English
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 English

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 All levels English
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 English
Learn the triangle congruence postulates which are the SAS, ASA, SSS, AAS, and HL. Each triangle postulate has a clear example with pictures, want to see?
5 minutes All levels English
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 All levels English
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 English
Learn how to translate a graph. Shifting, scaling and reflecting are three methods of producing graph translations for basic graphing functions.
5 minutes All levels English
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 All levels English
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 English
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 English
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 English
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 All levels English
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 All levels English
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 English
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 All levels English
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 All levels English
Learn the vertical angles definition and vertical angles theorem. Determine if vertical angles are congruent, adjacent, supplementary, or complementary angles.
5 minutes All levels English
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 All levels English
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 All levels English
Learn about tetrahedral in molecular geometry. We will cover a tetrahedral bond angle, shape, and structure in these examples. Want to see?
5 minutes All levels English

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 English
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 English
Learn how to find the perpendicular slope. When two lines intersect at right angles, they are perpendicular lines, and we can measure their slope.
6 minutes All levels English
Learn all the different types of polygons. Distinguish between regular and irregular polygons, simple and complex polygons, and concave and convex polygons.
6 minutes All levels English
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 English
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 All levels English
With this formula we will learn how to find the perimeter of a Quadrilateral. Then, we will apply knowledge of Quadrilaterals to calculate perimeter quickly.
6 minutes All levels English
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 English
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 English
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
A Dodecagon is a 12-sided polygon, with 12 interior angles, and 12 vertices which is where the sides meet. Want to find the area of a Dodecagon shape?
6 minutes All levels English
What is a Cuboid? We will cover the definition of a cuboid, review its shape, learn how to find the area of a cuboid, and it's properties. Want to see?
6 minutes All levels English

Similar Polygons

Learn the definition of similar polygons. Using similar polygons involves two mathematical concepts (similarity and polygons), and another concept, proportion.
6 minutes All levels English
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 English
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 English
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 the AA Criterion (Angle-Angle Criterion) definition, examples, proof, and more. All pairs of triangles with two congruent interior angles are similar.
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 English
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 All levels English
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
You may be wondering, is a parallelogram a quadrilateral? Learn how to prove a quadrilateral is a parallelogram in these examples. Want to see?
6 minutes All levels English
What is the quadratic formula? Learn the equation for the quadratic formula, examples, how to use the formula with steps, and when to use it. Want to see?
6 minutes All levels English

Transformations

Learn the types of transformations in math with definitions and examples. We will cover Geometry Transformations of shapes with their rules.
6 minutes All levels English
What is rotational symmetry? Shapes have rotational symmetry if they can be turned around their center less than one full rotation without appearing to change.
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
What is circumference? The definition of circumference is the distance around the circle. Two equations are used to find the circumference, want to learn?
5 minutes All levels English
Learn how to calculate the circumference of Earth step by step with examples. Want to see?
5 minutes All levels English
Learn how to find the diameter from the circumference, as well as converting circumference to diameter with this formula. Want to learn how?
5 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
What is the definition of an Arc in Geometry? An arc is a portion of a circle that is less than the entire circle. Learn how to measure and identify arcs.
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 English
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 All levels English
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 English
Learn how to find the area of a semicircle using this formula. Easily calculate the area and perimeter with this method.
6 minutes All levels English
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 All levels English
Learn how to find the area of sectors and segments of a circle using the area of a segment formulas. Want to learn the formulas?
6 minutes All levels English
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 English
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
What are 3D shapes? Examples of 3D shapes are dice, donuts, pyramids, beach balls, traffic cones. Let's take a closer look and the definition of 3D shapes.
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 English
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 English
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?

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