Section 10.2 Activities
Part A: Linear Angles
The angles [math]\angle ADC[/math] and [math]\angle BDC[/math] are called a [b]linear angle pair[/b]. [br]
#1
Using the [u][b]location[/b][/u]of the two angles to write a definition for a linear angle pair.[br][br][br]
#2
What do you observe about the angle measures of the linear angle pair?
#3
Make a conjecture about the sum of the measures of [u][b]any[/b][/u]linear angle pair.[br][br][br]
Part B: Vertical Angles
The angles [math]\angle AED[/math] and [math]\angle CEB[/math] are a vertical angle pair.[br]The angles [math]\angle AEC[/math] and [math]\angle DEB[/math] are a vertical angle pair.
#4
Based on the [u][b]location [/b][/u]of one of the vertical angle pairs above, write a definition for a vertical angle pair.
#5
Use points A, B, C, and D to change the angle values. Make a conjecture about the measures of a pair of vertical angles.[br][br][br]
Part C: Additional Angle Pairs
[b][color=#ff0000]Move the slider to the left so that it reads "Corresponding Angles." [/color][/b][br][br]The color-coded angle pairs below are made when a [b]transversal[/b] crosses two lines. These particular angle pairs are called [b]corresponding angles.[/b]
#6
Move one of the lines by dragging one of the points on the line. Notice that the pairs stay the same (the colors don’t change). When do the angle pairs seem the most equal in size?[br][br][br]
#7
Now, use the slider at the top of the screen to highlight some [u][b]different[/b][/u]angle pairs. (Not corresponding angles, but different angle pairs.) Define these pairs based on their location with respect to the transversal.[br][list=1][*]Alternate Interior Angles[/*][*]Alternate Exterior Angles[/*][*]Same Side Interior Angles[/*][*]Same Side Exterior Angles[/*][/list][br][br][br]
Part D: The Parallel Postulate
Lines [i]AB[/i] and [i]FC[/i] are [b]parallel[/b]. [br]Line [i]BC[/i] is called a [b]transversal [/b]of lines [i]AB[/i] and [i]FC[/i] because it transverses (crosses) the lines. [br] [br]Move the lines [i]AB[/i] and FC by moving points [i]A[/i], [i]B[/i], or [i]C[/i]. Notice as you do, that the lines [i]AB[/i] and [i]FC [/i][b][u]remain parallel[/u][/b]. Answer the following questions.
#8
What are the colored angled pairs called?
#9
What do you notice about the angle measures of the angle pairs?[br][br][br]
#10
Fill in the blanks below to define the Parallel Postulate:[br][i][br][b]Parallel Postulate:[/b][/i] When two ________________________ lines are cut by a _________________________________, the resulting __________________________________ angles are ______________________.[br][br][br]
#11
Use the Parallel Postulate to [b]prove [/b]that if two parallel lines are cut by a transversal, then the alternate interior angles are [u]congruent[/u]. (That is, c=f in the diagram above.)[br][br][br]
#12
Use the Parallel Postulate to [b]prove [/b]that if two parallel lines are cut by a transversal, then same side interior angles are [u]supplementary[/u]. (That is, c+e = 180[math]^\circ[/math] in the figure above.)[br][br]