Download 3.2 Day 1 HW

Name: _________________________________
Date: __________________
Period: ______
Geometer’s Sketchpad Introduction to 3.2
Directions:
1. Draw a line and label the two points on the line A and B.
Geometry w/ Trig
E
suur
2. Plot a point (label it C) not on AB .
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3. Draw a line through point C parallel to AB . (This can be done by
selecting C and AB . In the construct menu select “parallel line.”)
G
A
B
C
H
D
4. Plot a point on the new parallel line that contains point C. Label
this point D.
F
5. Draw a transversal line. Label the two points on the line E and F.
6. Construct the intersection of each parallel line with the
transversal. (Highlight one parallel line and the transversal. In the construct menu, select “intersection.”
Repeat for the second parallel line.) Label the intersections G and H.
7. Your sketch should look something like the above diagram.
8. Find the measure of all eight angles. (Select 3 points that form the angle, and select “angle” from measure
menu – the vertex must be the second point you select.) Drag each measurement so that it is located inside
the angle.
9. Name two pairs of alternate interior angles: ________________________________________________
10. What do you notice about the angle measures of each pair of alternate interior angles?
11. Name two pairs of alternate exterior angles: _______________________________________________
12. What do you notice about the angle measures of each pair of alternate exterior angles?
13. Name two pairs of corresponding angles: __________________________________________________
14. What do you notice about the angle measures of each pair of corresponding angles?
15. Name two pairs of consecutive interior angles: ___________________________________________
16. What do you notice about the angle measures of each pair of consecutive interior angles?
17. Move your transversal so that mAGE  90 . What do you notice about the measurement of CHG ?
18. Make some conjectures based on your Sketchpad Activity! Then use your new theorems/postulates to fill in
all seven missing angle measures in the diagram.
If two parallel lines are cut by a transversal, then each pair of…
Corresponding angles are __________________________.
Alternate interior angles are ________________________.
Alternate exterior angles are _________________________.
Consecutive interior angles are _______________________________.
In a plane, if a line is perpendicular to one of two parallel lines, then
___________________________________________________________________________________.
Get this paper checked by your teacher before continuing.
80°
Practice: Solve for the variable. State the theorem or postulate that justifies your reasoning.
1. If 2 II lines are cut by a transversal, then ________________________________________ are _________________________________.
(type of angles)
(≅/supplementary)
x = _______________
2. To solve for x: If 2 II lines are cut by a t, then ________________________________________ are _______________________________.
(type of angles)
(≅/supplementary)
To solve for y: If 2 II lines are cut by a t, then ________________________________________ are _______________________________.
(type of angles)
(≅/supplementary)
3. State TWO theorems/postulates used:
x = _______________, y = _______________
If _________________________________________________________, then ______________________________________________________________.
If _________________________________________________________, then ______________________________________________________________.
y = _______________
4. **Challenge! Solve for x, y, and z.
x = _______________, y = ______________, z = ______________