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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.

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Inductive reasoning is used to form hypotheses, while deductive reasoning can be helpful in solving geometric proofs. Want to see the video?

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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?

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In geometry, three undefined terms are the underpinnings of Euclidean geometry: point, line, and plane. Want to see the video?

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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?

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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?

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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!

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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.

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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?

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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?

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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?

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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.

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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?

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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.

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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.

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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?

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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?

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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?

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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.

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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.

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What is geometric construction? Geometric construction allows you to construct lines, angles, and polygons with a compass and straightedge using these methods.

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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.

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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?

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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.

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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
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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.

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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.

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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?

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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?

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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?

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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
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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.

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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?

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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.

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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?

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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
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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?

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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.

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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?

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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
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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
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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.

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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.

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Learn the vertical angles definition and vertical angles theorem. Determine if vertical angles are congruent, adjacent, supplementary, or complementary angles.

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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.

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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
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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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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
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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
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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
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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
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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?

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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.

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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
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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?

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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.

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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?

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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
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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.

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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
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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
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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
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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
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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
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Learn how to solve proportions. Easy step-by-step examples to solving proportions. Want to check out the video and lesson?

6 minutes
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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
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Learn and apply the Triangle Proportionality Theorem to common situations encountered in daily life. Want to check out the video and lesson?

6 minutes
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Learn and apply Heron's Formula for finding the area of a triangle in this lesson. Want to check out the video?

6 minutes
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What is an irregular quadrilateral? Irregular quadrilaterals are: rectangle, trapezoid, parallelogram, kite, and rhombus. Learn the definition and area here.

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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
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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
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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
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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
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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.

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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
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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
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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
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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
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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
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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
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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
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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
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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
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English

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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