Discovering
Line Properties
This is a prototype of JavaSketchpad,
a World-Wide-Web component of The
Geometer's Sketchpad. Copyright ©1990-1998 by Key
Curriculum Press, Inc. All rights reserved. Portions of this work
were funded by the National Science Foundation (awards DMI
9561674 & 9623018).
Inverstigation
1.1 Intersecting Lines
- Observe the measure of angles CAD, BAC, EAB, and EAD.
What do you notice? Drag points B. C, D and E. Do your
findings still hold true? What can you say about the
vertical angles EAD and BAC? What can you say about the
adjacent angles EAD and EAB?
- Is it possible for these adjacent angles to be equal? If
so, when?
- If you only knew the measure of one angle , would it be
possible to find the other three? Why or why not?
- What if you had three lines intersecting at the one
point. How many angle measurements would you need in
order to find the rest?
- Write your findings in the form of a conjecture(s).
Investigation
1.2 Parallel Lines cut by a Transversal.
Note: Parallel lines DE and GB were
constructed and intersected by another line (HF).
- Observe the corresponding angles GAH and DCA. Why are
these angles called corresponding angles? What do you
notice about their measures? Drag points D, F, E, G, B,
or H to confirm your findings.
- Observe the alternate interior angles DCA and CAB. Why
are these angles called alternate interior angles? What
do you notice about their measures? Drag points D, F, E,
G, B, or H to confirm your findings.
- Observe the alternate exterior angles GAH and FCE. Why
are these angles called alternate exterior angles? What
do you notice about their measures? Drag points D, F, E,
G, B, or H to confirm your findings.
- Observe the adjacent angles GAH and GAC. Why are these
angles called adjacent angles? What do you notice about
their measures? Drag points D, F, E, G, B, or H to
confirm your findings.
- Write your findings in the form of a conjecture(s).
Investigation
1.3 Slope of Parallel Lines
- Observe the measure of the slope of line a and line b. What
do you notice? Drag points D, F, E, G, A or B . Do your
findings still hold true?
- Write your findings in the form of a conjecture?
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