Angles and Their Measurements
Besides a protractor, Geogebra has its own embedded [color=#ff0000]ANGLE measurement tool[/color]. Let's go ahead and use it as we start developing our common vocabulary terms. It is the top tool in this list of tools and looks like the following:
[b]NOTE: WHEN WE TALK ABOUT AN ANGLE'S MEASURE in this course[/b], [b]we are primarily referring to the measurement that is 180[/b][math]^{\circ}[/math][b] or less. [/b]When we refer to [math]\angle[/math]BAC or [math]\angle[/math]CAB, we are referring to the same angle ([color=#ea9999]see the pink angle below[/color]). In GeoGebra, you need to click on the three points in a specific order. If you click with the [color=#ff0000]Angle tool[/color] on [color=#38761d]B->A->C it will measure the angle marked in green[/color] vs. [color=#ea9999]C -> A -> B it will measure the angle in pink[/color] as shown in the diagram below.
B->A->C in Green and C -> A -> B in Pink
[size=150]The [color=#ea9999]pink angle[/color] is the one that we are seeking.[/size]
[b][size=150][size=200]INSTRUCTIONS FOR TASK:[/size][/size][/b][br][b]Goal: [/b]Measure [math]\angle[/math]CAB.[b][br]Step 1: [/b]Select [color=#ff0000]Angle Tool[/color]. The "Vertex" point of the angle should be selected as the second point. [br]Click on C -> A -> B .
[size=150][b][size=200]INSTRUCTIONS FOR TASK:[/size][/b][/size][br][br]Measure the [b][i]straight angle[/i][/b] [math]\angle[/math]ABC.
[b]Fill in the blank (Don't forget to copy this definition into your math notebook). [br][br]DEFINITION:[/b][br] [b]Straight Angle[/b] - If an angle measures __________________, then it is called a [b][i]straight angle[/i][/b].
[size=150][b][size=200]INSTRUCTIONS FOR TASK:[/size][/b][/size][br][br][b]Step 1: [/b]Measure [math]\angle[/math]C.[br][b]Step 2: [/b]Measure [math]\angle[/math]EBA.
Both [math]\angle[/math]C and [math]\angle[/math]EBA are [b][i]right angles[/i][/b]. [br][b][br]Fill in the blank (Don't forget to copy this definition into your math notebook). [br][br]DEFINITION:[/b][br] [b]Right Angle[/b] - If an angle measures __________________, then it is called a [b][i]right angle[/i][/b].
Segment AC is perpendicular to Segment CD. Line EB is perpendicular to AB.[br][b][br]Fill in the blank (Don't forget to copy this definition into your math notebook). [br][br]DEFINITION:[/b][br] [b]Perpendicular[/b] - If lines (rays or segments) form __________________ angles, then they are [b][i]perpendicular[/i][/b].[br][br]Note: The symbol for perpendicular is [math]\perp[/math].