Judith Coutts
Westwood Regional Jr/Sr. High School

TOPIC:

LEVEL:

GSP PROFICIENCY:

CLASS TIME:

CONSTRUCTION GUIDE:

CONSTRUCT THE LINES

1. On Display choose Preferences...1. Arrowheads for rays and lines. 2. Put and X in the box for Autoshow labels for Points; and the box for Straight Objects. 3. Distances units -inches; Precision -tenths. 4. Angle units - degrees; precision - tenths. 5. Calculations - Precision - hundredths. 5.Again on Display choose Line Weight ...Thick Lines and Color...red.

2. Choose the LINE TOOL from the tools. DRAW oblique line AB.

3. DRAW another oblique thick red line CD that does not intersect on the screen but that does not appear parallel to the thick red line AB.

4. DRAW a transversal, that is, a line which intersects both of the others. This line will have small boxes on it to show that it is SELECTED. Display Color...Blue; Line Weight...Thin

5. Construct the two Points at intersection using the following directions. Choose the ARROW (the SELECT TOOL) from the tools and with the SHIFT down click the ARROW on red line AB. Both the thin blue line EF and thick red line AB will be selected. From the Construct menu choose Point at intersection . Using the SHIFT key, SELECT the thin blue line EF and the other thick red line CD. Construct the point at intersection of these two lines

6. If necessary, with the SELECT Tool arrange the points on the thick red lines so that they are on both sides of the transversal as shown. Use the HAND(A) tool (DOUBLE CLICK) to change labels to those in guide. SINGLE CLICK to drag the labels of lines to the boundaries of the diagram.

MEASURE THE ANGLES

7. With the SELECT Tool, SELECT the three points of an angle whose vertex is one of the points at intersection. With SHIFT down, SELECT point E, point G and point B. On the Measure menu choose Angle. Repeat to Measure each of these eight angles with vertex G or H. SELECT each angle measure and move to its appropriate place.

OBSERVATION WORKSHEET

NAME _____________________________ CLASS________________________

1. Name four pairs of angles which have the same measure ____________________________
From the diagram, what kind of angles are these angles? ________________________

2. Name eight pairs of angles which are supplementary ________ _______
From the diagram what kind of angles are these supplementary angles? _______________________

CONCLUSIONS

• From Observation #1: If two angles are _______________,then they are equal.
• From Observation #2: If two angles are _________________,then they are supplementary.

Using the SELECT tool, SELECT Point H. On the Transform menu choose Mark Center H. At the top of the tools, choose the ROTATE tool (CLICK on the ARROW and move right to the ROTATE tool.) With this ROTATE TOOL selected, ROTATE the thick red line CD until there are only two different angle measures showing.

3. What do your notice about the thick red lines lines? __________________________

SELECT thick red line AB (j), Measure its Slope. Measure the slope of thick red line CD(k).
Slope line AB(j) =_______ . Slope Line CD(k) =_______

4. What do you observe? ___________________________________

SELECT thick red line CD(k) and point G on the thick red line AB(j). Construct a Parallel line.. Display Color...Green.

5. What happens? _________________________________________

CONCLUSIONS

• From Observation #3. If Corresponding angles are equal then the coplanar lines cut by a transversal are ____________.
• From Observation #4: If two lines are parallel then they have______________ .
• From Observation #5: Since the new line is constructed parallel and is the same line as the thick red line AB (j), then thick red line AB (j) must also be parallel to CD (k).

ROTATE the thick red line CD so that the angle measures = 90.

6. According to the definition of __________, thick red line CD is now in what relation to the thin blue transversal, EF (m)? ____________ ________

7. What appears to be true of the relationship of the thin blue transversal, EF to the green line (n)? ________________

CONCLUSIONS

• From Observation #6: If two lines intersect to form 90 degree angles,then they are _____________.
• From Observation #7: If a line is perpendicular to one of two parallel lines, then it is ________ to the other also.

SELECT point G. Transform and Mark Center G. ROTATE thick red line AB so that the angle measures = 90.

8. What is the slope of each of the thick red lines?
Slope line AB (j) = _______ Slope line CD (k) = _____.

9. What does this indicate?_________________________________

10. Line AB (j) and the green line (n) are both parallel to line CD (k). What is the relationship of thick red line AB (j) and green line(n) ? _________________

CONCLUSIONS

• From Observation #9: If two lines have the same slope, then______ ___________.
• From Observation #10:If two line are parallel to the same line, then they are _____________.

SELECT the thin blue line EF (m) and Measure its Slope.

11. How does the sign of the slope of the thin blue line EF (m) compare to the slopes of the thick red lines AB (j) and CD (k)?_______________

12. On your calculator take the reciprocal of the slope of line AB (j). What do you notice? ______________________________

13. SELECT both the measure of the slopes of the thick red line AB(j) and of the thin blue line EF(m). On the Measure menu, Calculate Slope of line j x Slope of line m. What is this Product?_______________

CONCLUSIONS

• From Observations #11 and 12: If two lines are perpendicular, then their slopes are ___________.
• From Observation #13. The product of the slopes of perpendicular lines is_________________

Discuss your results with your group and study UCSMP Geometry chapter 3. Make a list of all of the titles of the postulates, theorems and definitions you have explored. Extra plus for the group that can demonstrate additional postulates, definitions or theorems using GSP.

NOTES TO TEACHER:

Student will explore or review most of the important ideas in chapter 3.

The instructions try to take advantage of the color display, as well as the geometry notation since the students sometimes lose the labels in their manipulations. The thick, thin notation is for those without color monitors.
Exploring Geometry published by Key Curriculum Press,1993, has two investigations which are also very helpful in chapter 3.

• Angles Formed by Intersecting Lines(61)
• Properties of Parallel Lines (pg.63)