[b][code][/code]Step 1:[/b] Click this angle bisector icon [icon]https://www.geogebra.org/images/ggb/toolbar/mode_angularbisector.png[/icon]and then click the points A, B and C in that order to draw the angle bisector for [math]\angle[/math]ABC.[br][b]Step 2: [/b] Click this intersection icon [icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon] and then choose the angle bisector line and AC. You should see a new point at the intersection.[br][b]Step 3: [/b] To label the new point, click the label icon [icon]/images/ggb/toolbar/mode_showhidelabel.png[/icon] and the new point. It should say D. If not, restart and redo steps 1-3.[br][b]Step 4:[/b] Measure the bisected angle using [b][icon]https://www.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon] [/b]and clicking on 3 points making sure that the vertex is the middle one.[br][b]Step 5:[/b] Using the [icon]/images/ggb/toolbar/mode_move.png[/icon] drag around point C on the triangle to make sure that the line you drew always bisects the angle into two equal halves.[br][b]Step 6: [/b]Have your teacher check your work before moving to the next section.
[b]Step 7:[/b] Click on segment measurement icon [icon]/images/ggb/toolbar/mode_distance.png[/icon] and the points A and B to show the length of AB.[br][b]Step 8: [/b]Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_distance.png[/icon] to also show the lengths of BC, AD and DC.[br]
Use [icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon] to move point C so that AB = BC. What do you notice about AD and DC?
Now move point C so that AB is longer than BC. What do you notice about AD and DC? Now move point C so that AB is shorter than BC. In the space below, describe what you noticed.
Now move point C so that BC is the same length as DC. What do you notice about BC and DC?
Which of the following is [b][u]not[/u][/b] a ratio that is always equal?
[img]https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTqFF_MA8VBXvn8BDKpIvzH0gxuEyAtSZB9CYj1CHOTh1hKGTpO&s[/img]
Use this applet to discover the angle bisector proportionality theorem!
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[/img]
[img]https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQsXTfj4b08LRms3zYna8wuqZrrMIkZOOUXBDzxilPahoJynP7T2A&s[/img]