Intro to Geogebra
What is Geogebra?
Geogebra is an online tool that we can use to help us with Geometry.
Shapes in Geogebra
Here are a few different shapes made in Geogebra. Move the points that are blue around, and see what happens.
What can you do with Geogebra?
Geogebra allows us to create geometric shapes, measure them, and manipulate them.
Make lines
[list=1][*]Make a [u]line[/u] that goes through points A and B.[br][/*][*]Make a [u]segment[/u] that goes through points C and D.[/*][*]Make a [u]ray[/u] that starts at E and passes through F.[/*][/list]
Make circles.
Make a circle in three different ways.[br][list=1][*]Make a circle with a centre that goes through a point.[/*][*]Make a circle with a centre and a radius of 2.[/*][*]Make a circle that goes through three points.[/*][/list]
Measure lines
Select the Distance or Length tool.[br][br]Now click on the point A, and then B.
Measure angles
Below are points A, B and C. Find [math]\angle[/math]ABC with the Angle tool by clicking A, B then C.
Tangents
What is a tangent?
A tangent of a circle is a line that touches the circle at exactly one point.[br][br][color=#6d9eeb]The blue circle on the left[/color] has a tangent on it, and[color=#93c47d] the green circle on the right [/color]has a line going through the circle, but it is not tangent to the circle.[br][br]The point T is called [i]the point of tangency[/i].
Find the tangent.
A circle is given below, with centre C, radius r. The radius r meets the circle at point P.[br][br]Draw a tangent line at the point P, and add a point on the tangent.[br][br]What is the angle between the tangent and the radius?
Using the Pythagorean Theorem with tangent lines.
We know that the angle between the radius and tangent is 90ยบ, and the Pythagorean Theorem tells us about right angle triangles. Consider this problem.[br][br]The line AB is tangent to the circle below, with A the point of tangency.[br][br]The radius (AC) has length 4, and the line AB has length 7.[br][br]What is the length of the line BC?