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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

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:

$f(x) = ax + b$
$f(x) = ax^2 + bx + c$

$y = mx + b$

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

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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