Download PreCalculus AB

Honors Geometry
_________________________
Name
Investigation with Angles and Lines
SKETCHPAD
1.
Using Sketchpad, draw intersecting lines.
2.
Construct enough points (5) to label all of the angles shown. (Note that your
angles will not be called < 1,<2, <3, and <4.)
3.
Measure all 4 angles, and record your results below.
4.
Record 3 sets of measurements. (Record a set, move one of the lines, record
measurements again, move one line, and record the measurements again.
m< 1 =
m< 1 =
m< 1 =
m< 2 =
m< 2 =
m< 2 =
m< 3 =
m< 3 =
m< 3 =
m< 4 =
m< 4 =
m< 4 =
5.
Save your Sketchpad document as ANGLESLINES. I may ask to see your
document in class.
6.
CONJECTURES. Based on the measurements above, fill in these relationships.
a)
Linear pairs are _________________.
b)
If two angles are supplementary to the same angle, then those two angles
are __________ to each other.
c)
Vertical angles are ___________.
Angles and Lines Investigation
page 2
7.
Using Sketchpad, construct PQ  PS and PR  PT
8.
Measure all of the angles three times, as you did in the investigation above.
m< 4 =
m< 4 =
m< 4 =
m< 5 =
m< 5 =
m< 5 =
m< 6 =
m< 6 =
m< 6 =
9.
Save your Sketchpad document as PERPPAIRS.
10.
CONJECTURES. Based on the measurements above, fill in these relationships.
11.
a)
Perpendicular pairs are ______________________.
b)
If two angles are complementary to the same angle, then they are
___________ to each other.
Using Sketchpad, construct four angles with none of them adjacent.
Angles and Lines Investigation
12.
page 3
Adjust the angles so that their measurements produce < 2  < 4.
Adjust < 1 so that < 1 is supplementary to < 2, and adjust < 3 so that
< 3 is supplementary to < 4.
13.
Save your Sketchpad document as SUPPPAIRS.
14.
How are < 1 and < 3 related? ________________
15.
CONJECTURE. Based on the measurements above, fill in these relationships.
a)
If two angles are supplementary to two congruent angles, then those two
angles are _________ to each other.
b)
If “supplementary” is replaced by “complementary” in the conjecture
immediately above, would the conclusion be the same?
c)
If “supplementary” is replaced by “congruent” in the conjecture
above, would the conclusion be the same?