Index of GeoGebra Activities

Circles Functions Geometry
Relations Trigonometry

Circles

Angle Inscribed in Semicircle

  • Show that an inscribed angle subtended by a semicircle is always equal to 90 degrees
Central and Inscribed Angles

  • Show that inscribed angles are half the measure of the central angle subtended by the same arc
Chord Perpendicular Bisector

  • Show that the perpendicular that bisects a chord goes through the centre of the circle
Cyclic Quadrilateral Opposite Angles

  • Show that opposite angles in cyclic quadrilaterals are supplementary
Inscribed Angles

  • Show that inscribed angles subtended by the same arc are equal
Tangent at Radius

  • Show that a tangent to a circle is perpendicular to the radius at the point of tangency
Tangents to at Point

  • Show that tangent segments to a circle, from any external point, are congruent

Functions

Absolute Value

  • Show how the graphs of f(x) and |f(x)| relate to each other
  • Choose from:
    • f(x) = a(x - b)
    • f(x) = a(x - b)(x - c)
Absolute Value - Draggable

  • Show how the parameters in y = mx + b are related to the characteristics of the corresponding graph
  • f(x) is defined by draggable points
  • Choose from:
    • f(x) = ax + b
    • f(x) = ax^2 + bx + c
Linear - y = mx + b

  • Show how the parameters in y = mx + b are related to the characteristics of the corresponding graph
Quadratic - Expanded Form

  • Show how the parameters in f(x) = ax^2 + bx + c are related to the characteristics of the corresponding graph
Quadratic - Factored Form

  • Show how the parameters in f(x) = a(x - b)(x - c) are related to the characteristics of the corresponding graph
Quadratic - Vertex Form

  • Show how the parameters in f(x) = a(x - p)^2 + q are related to the characteristics of the corresponding graph
Reciprocal - Polynomials

  • Show how the graphs of f(x) and \frac{1}{f(x)} relate to each other
  • Choose from:
    • f(x) = a(x - b)
    • f(x) = a(x - b)(x - c)
Reciprocal - Polynomials - Draggable

  • Show how the graphs of f(x) and \frac{1}{f(x)} relate to each other
  • f(x) is defined by draggable points
  • Choose from:
    • f(x) = ax + b
    • f(x) = ax^2 +bx + c
Stretches - Practice

  • Given a random function and a random stretch of that function (of the form g(x)= af(bx)), determine what a, b must be
  • Watch the individual stretches to see if your a, b values are correct
  • Keep practicing with random functions
Transformations - Animation

  • Enter values for a, b, h, k and click buttons to watch the individual transformations of g(x)= af(b(x-h))+k separately
  • For negative a and b values, watch the stretch, then see the reflection
  • Also see how a moveable point gets transformed
  • Choose from the following functions:
f(x) = x f(x) = x^2 f(x) = x^3
f(x) = \sqrt{x} f(x) = 10^x f(x) = \log_{10}{x}
Transformations - Animation - Piecewise

  • Enter values for a, b, h, k and click buttons to watch the individual transformations of g(x)= af(b(x-h))+k separately
  • For negative a and b values, watch the stretch, then see the reflection
  • f(x) is a piecewise function defined by draggable points
  Transformations - Practice

  • Given a random function and a random transformation of that function (of the form g(x)= af(b(x-h))+k), determine what a,b,h,k must be
  • Watch the individual transformations to see if your a,b,h,k values are correct
  • Keep practicing with random functions
Transformations - Sliders

  • Use sliders to show how the graph of g(x)= af(b(x-h))+k is related to the graph of f(x)
  • Also see how a moveable point gets transformed
  • Choose from the following functions
f(x) = x f(x) = x^2 f(x) = x^3
f(x) = \sqrt{x} f(x) = 10^x f(x) = \log_{10}{x}
Transformations - Sliders - Piecewise

  • Use sliders to show how the graph of g(x)= af(b(x-h))+k is related to the graph of f(x)
  • f(x) is a piecewise function defined by draggable points
Translations - Practice

  • Given a random function and a random translation of that function (of the form g(x)=f(x?h)+k), determine what h,k must be
  • Watch the individual translations to see if your h,k values are correct
  • Keep practicing with random functions

Geometry

Opposite Angles

  • Show that opposite angles formed by two intersecting lines are equal
Parallel Lines and Transversal

  • Show the angle relationships associated with two parallel lines and a transversal
  • Show the naming of angle pairs formed by two lines and a transversal
Quadrilaterals - Sum of Angles

  • Show that the sum of interior angles in any quadrilateral is 360 degrees
Slope

  • Show how slope can be calculated for line segments
  • Slope can be calculated using either \frac{Rise}{Run} or \frac{y_2-y_1}{x_2-x_1}
Triangles - Sum of Angles

  • Show that the sum of interior angles in any triangle is 180 degrees

Relations

Domain and Range Shadows

  • Show that the range can be thought of as the shadow of the graph projected onto the y-axis
  • Show that the domain can be thought of as the shadow of the graph projected onto the x-axis

Trigonometry

Similar Triangles

  • Show that any two triangles with two angles equal will be similar
  • Show that the Sine, Cosine, and Tangent ratios are direct consequences of triangle similarity
Sine Law

  • Show the geometric implications of the Sine Law
Sine Law - Ambiguous Case

  • Show how 0, 1, or 2 triangles can be constructed when given two sides and a non-contained angle

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