# Index of GeoGebra Activities

## 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
• Show how the parameters in $$f(x)=ax^2+bx+c$$ are related to the characteristics of the corresponding graph
• Show how the parameters in $$f(x)=a(x−b)(x−c)$$ are related to the characteristics of the corresponding graph
• 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