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Angle Bisector Theorem


Geometry 
The angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. 


Box Rotation around a Point


Geometry 
Graph demonstrates how to rotate a box around a point using trigonometry. 


Building Equations from Rectangles


Equations 
PreAlgebra: Build equations by turning on width or height and area. Or build equations by turning on width or height and perimeter.
Algebra 1: Build and solve a quadratic equation by turning on area and perimeter. 


Calculating Correlation Coefficient


Statistics 
Graph helps visualize the correlation coefficient relationship between two variables. 


Calculating Pi with Calculus


Calculus 
Pi may be calculated by finding the area under a halfcircle, then solving for pi using the area of a circle. 


Calculating Pi with Perimeter


Number Theory 
π may be calculated by inscribing a regular polygon into a circle. By measuring perimeter, π may be estimated. 


Calculating Sample Variance and Standard Deviation


Statistics 
Variance measures how far a set of numbers is spread out from their average value. This model represents the calculation of sample variance. 


Circumcenter Theorem


Geometry 
Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. 


Color Theory (CMYK)


Geometry 
Any color you see on a surface is formed by the subtractive color mixing model. We are more familiar with this color model because it is how we learned to mix colors. In this case, “subtractive” refers to removing the light from the paper by adding more color. "K" represents blacK which is added in the printing process to make the colors more realistic. 


Color Theory (RGB)


Art 
Mixing light—or the additive color mixing model—allows you to create colors by mixing red, green and blue light sources of various strengths. The more light you add, the brighter the color becomes. If you mix all three colors of light, you get pure, white light. 


Color Wheel


Art 
Explore the color wheel. Adjust for complementary, analogous, and triadic colors. 


Compound Interest Visual Calculator


Finance 
Graph compares simple, compound, and continuous interest. 


Cyclic Quadrilateral


Geometry 
Angles formed by an inscribed quadrilateral form distinct relationships. 


Electromagnetic Spectrum


Physics 
Graph describes visually the visible light in the electromagnetic spectrum. 


Electromagnetic Spectrum (frequency chart)


Physics 
This visual graphic can be modified to add labels describing different frequencies. 


Excircle Triangle Properties


Geometry 
An excircle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Diagram displays one of the three triangles tangent to the circle. The center of an excircle is the intersection of the internal bisector of one angle (at vertex 


Fahrenheit and Celsius


Linear Equations 
Use a linear function to convert temperatures. 


Focus and Directrix of Parabola


Functions 
A parabola is moves in a plane where its distance from a fixed point known as a focus is always equal to the distance from a fixed straight line known as directrix. 


Function Average


Calculus 
Function average is y value where the area between a and b is equal to the area under the curve. 


Golden Mean Measurement


Number Theory 
Use the Golden Mean to find natural relationships in art, architecture, and nature. 


Incenter Theorem


Geometry 
The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. 


Infinite Geometric Series of 1


Sequences and Series 
Graph describes the sum of the infinite geometric series of 1, 


Inscribed Triangle Angles


Geometry 
Angles formed by an inscribed triangle and a tangent line from one of the triangle points form distinct relationships. 


Interior Angle of Regular Polygon


Geometry 
N the function f(x) below, x = number of sides in a regular polygon. The function solves for the interior angle. What is the limit for y when x > 0? Does this mean that the interior angle inside a circle (when n = ∞) is a straight line? 


Intersecting Chords


Geometry 
Length of chords intersecting in a circle can be calculated through proportional relationships. 


Inverse Variation


Functions 
Equations for Inverse Variation. k is the constant of proportionality. Graph is a rational function. 


Measuring Random Angles


Geometry 
Students can randomly generate angles and measure them with a digital protractor. 


Midsegment Theorem


Geometry 
The Midsegment Theorem states that the midsegment connecting two midpoints of a triangle is parallel to the third side of the triangle. The length of the midsegment is also half the length of the third side. For example, the midsegment of two midpoints could have a length of 4. This would mean that the length of the third side is 8 and the two lines are parallel. The midsegment is always half the length of the third side. Conversely, the third side is always twice as long as the midsegment. 


Midsegment Theorem


Geometry 
The segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side. 


Normal Distribution


Statistics 
Normal distributions are often used in the natural and social sciences to represent realvalued random variables of which the distributions are unknown. 


Outside Angle Theorem (Two Tangents)


Geometry 
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then the angle formed from the intersecting tangent lines is equal to 180 degrees minus the angle of the far arc. 


Pascal's Triangle


Number Theory 
Pascal's Triangle is a structure he develop that has interesting characteristics. 


Pendulum


Physics 
Simple Pendulum. t is time. l is the length of the pendulum. f(x) is the simple harmonic oscillator equation. 


Percent Error and Greatest Possible Error


Precision 
Percent error is the greatest possible error divided by the measurement multiply by 100%. The greatest possible error is equal to 1/2 of its precision. 


Perpendicular Segment in a Circle Law


Geometry 
Perpendicular lines from the center of a circle to a chord will always bisect the chord. Angles formed from two points on the circumference are equal to other angles. 


Proportional Relationships


Ratios 
Diagram visualizes proportional relationships. 


Pythagorean Theorem


Geometry 
Provides calculation methods for Pythagorean Theorem. 


Pythagorean Theorem


Geometry 
Graph displays Pythagorean Theorem in visual form. 


Quadratic Function


Functions 
Use this graph to analyze the characteristics of a quadratic function. 


Regular Hexagon from Congruent Circles


Geometry 
A regular hexagon may be constructed from congruent circles that pass through the circle centers. 


RGB Color Creator


Art 
Students will use hexadecimal values to define 3 x 8bit RGB colors. 


Rhombus Properrties


Geometry 
Diagonal bisector of a rhombus create a pair of opposite angles. The diagonals of a rhombus are perpendicular. 


Riemann Sum


Calculus 
A Riemann sum is a certain kind of approximation of an integral by a finite sum. 


Riemann Sum


Calculus 
A Riemann sum approximates an integral by a finite sum. 


Rotation of a Polygon (90degree)


Geometry 
Notice how the x and y values are negated or reversed for rotation at 90 degrees. Load graph in Desmos to view values. 


SecantSector Relationships


Geometry 
A) The measure of an angle formed by two secants intersecting outside a circle is half the difference of the arcs intercepted by the angle.
B) The measure of an angle formed by two intersecting chords is onehalf the sum of the measures of the arcs intercepted by it and its vertical angles. 


SecantTangent Theorem


Geometry 
If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. 


Simple Calculus Demo


Calculus 
This demonstration illustrates the relationship between a derivative function and the area below a function. 


Standing Wave in a Tube


Physics 
Standing wave in open tube. Air molecules are described as dots. 


Three Overlapping Similar Triangles


Geometry 
Two right triangles are similar if the corresponding sides are proportional to each other, and the corresponding angles are congruent. In this case, all three nested triangles are similar. 


Tranforming Triangles Using Matrices


Matrices 
Transformation matrices are used extensively in computer graphics. Learn how a transformation matrix affects a polygon by adjusting values in the matrix. See what happens when you perform a transformation with an identity matrix. Drag the blue and red points to affect the transformation matrix. 


Transforming Sinusoidal Functions


Trigonometry 
Graph may be used to understand how sinusodial functions are transformed. 


Trapezoid Median


Geometry 
The median of a trapezoid is parallel to each base and the length of the median equals onehalf the sum of the lengths of the two bases. 


Twelve Functions

