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 a 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 graphs of \( f(x) \) and \( |f(x)| \) relate to each other
  • \( f(x) \) is defined by draggable points
  • Choose from:
    • \( f(x)=ax+b \)
    • \( f(x)=ax^2+bx+c \)
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 \( \frac{y2 - y1}{x2 - x1} \)
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 equal angles 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