Download Lines and Their Relationships Performance Task

GEOMETRY
Unit 3
APPENDIX 3B
Name _________________________ Date: _______________ Block: ___________
PERFORMANCE TASK 1
Geometry Unit 3 – Lines and Their Relationships (no rubric)
1. Open a new sketch.
2. Set your preference measures.
 Point/Click on Edit.
 Scroll down and point/click on PREFERENCES.
 Change degrees to units, change Distance to
Tenths, change Slope.. to Tenths, and be sure
to click the box for NEW SKETCHES.
 Point/Click on OK.
3. Construct:
 Using your LINE tool, construct a line near the top of your screen.
 Click on a white part of the screen.
 Using your POINT tool, construct a point somewhere below your line, leaving
about an inch or two of space in between.
 Using your arrow tool, click on the point and the line.
 Go to CONSTRUCT and choose Parallel Lines.
4. Investigate:
 Using your arrow tool, click on a white part of the screen.
 Click on either one of the lines and holding down your mouse, move the line.
Click on one of the points on the first line and move your mouse.
 What do you notice about the two lines as you move the mouse?
Explain what you think is happening.
5. Measure and Compare:
 Click on a white part of the screen to deselect everything.
 Click on one of the parallel lines, go to Measure and choose Slope.
 Click on a white part of the screen, and then measure the slope of the second
line.
 What do you notice about the slopes of the two lines? Explain why.
6. Construct:
 Draw a segment that intersects both parallel lines.
 This segment is called a TRANSVERSAL…based on what you see, explain
what you think a TRANSVERSAL is.
K. Greenhaus ©2006
Virginia Beach City Public Schools/Department of Curriculum and Instruction/2006
1
GEOMETRY
Unit 3
APPENDIX 3B







Using your arrow tool, select the segment and ONE of the parallel lines.
Go to Construct and choose Intersection.
Click on a white part of the screen, and then select the segment and the
OTHER line.
A
B
Go to Construct and choose Intersection.
D
E
F
Using your point tool, construct points on each of the
parallel lines so that you have a point on each line on
EITHER side of the transversal segment.
Using the ‘A’ tool, click on the points and label them. Make sure to start with
the top line, clicking on the points from left to right. Points should be labeled
A, B, C (top line), and D, E, F (bottom line).
Label the endpoints of your segment G and H.
1.
Measure all the angles:
 Using the arrow tool, measure all the angles created (total of 8). Remember,
to measure an angle, click on the three points that make the angle, making
sure the VERTEX is the SECOND point you click on.
 Example: To measure <ABG, click on point A, then point B (vertex0, then
point G using your arrow tool, then go to Measure and choose Angle.
 Measure all 8 angles and using your arrow tool, move each angle measure
near the angle it actually measures.
 What do you notice about the angle measure?
2.
Investigate:
 Click on a white space on the screen.
 Using your arrow tool, click on either point H or point G and move the
transversal. Notice what happens to the angle measures.
 Click on the lines or points on the line and move the parallel lines. Notice
what happens to the angle measures.
 Write down a conclusion about the angle measures based on what you
noticed as you moved parts of your picture.
K. Greenhaus©2006
2
Virginia Beach City Public Schools/Department of Curriculum and Instruction/2006
C
GEOMETRY
Unit 3
APPENDIX 3B
9. Definition Explorations:
 Using your sketch with the angle measures and parallel lines, make
conjectures for the following (move things around in your sketch to verify what
you are writing down as a conjecture):
1. The following angle pairs are called CORRESPONDING ANGLES:
<ABG AND <DEB; <ABE and <DEH; <GBC and <BEF; and <CBE and
<FEH. Based on what you see in your sketch, write a conjecture
about what corresponding angles are and what type of
relationship they appear to have:
2. The following angle pairs are called ALTERNATE INTERIOR
ANGLES: <ABE and <BEF; and <CBE and <DEB. Based on what
you see in your sketch, write a conjecture about what alternate
interior angles are and what type of relationship they appear to
have:
3. The following angle pairs are called SAME SIDE INTERIOR
ANGLES: <ABE and <DEB; and <BEF and <CBE. Based on what
you see in your sketch, write a conjecture about what same side
interior angles are and what type of relationship they appear to
have:
4. The following angle pairs are called ALTERNATE EXTERIOR
ANGLES: <ABG and <FEH; and <GBC and <DEH. Based on what
you see in your sketch, write a conjecture about what alternate
exterior angles are and what type of relationship they appear to
have.
K. Greenhaus©2006
Virginia Beach City Public Schools/Department of Curriculum and Instruction/2006
3
GEOMETRY
Unit 3
APPENDIX 3B
10. Conjecture Verification:
 Using your point tool, put a point on transversal GH between point E and H.
 Using your ‘A’ tool, label the new point I.
 Using your arrow tool, click on point I and line DF, go to Construct and
choose Parallel Line – you should now have a third parallel line.
 Using your point tool to put two points on your new line, one on either side of
point I. label your new points J & K.
 Based on your conjectures made in 11, predict what the measures of the
following angles will be WITHOUT actually measuring:
o <EIJ _________________ Why?
o <JIH _________________ Why?
o <EIK _________________ Why?
o <KIH _________________ Why?


Using your arrow tool, measure the four angles < EIJ, <JIH, <EIK and <KIH.
Were the measurements what you predicted? ____________ Are your
conjectures about same side interior, alternate interior, alternate
exterior and corresponding angles correct?
11. Final Conclusions:
 Make a final conclusion about the angles formed when parallel lines are cut
by a line (segment) called a transversal:
***Bring this completed worksheet with ALL questions answered, back to the
classroom for further discussion and reflection. See if you notice any
relationships between sides, angles and lengths.
K. Greenhaus©2006
4
Virginia Beach City Public Schools/Department of Curriculum and Instruction/2006
GEOMETRY
Virginia Beach City Public Schools/Department of Curriculum and Instruction/2006
Unit 3
5