Name: ______Date: ______Hr: ______
Geometry Unit 3: Worksheet #1
1. What does it mean for two lines to be parallel? Explain and draw a pair of parallel lines.
2. What does it mean for two lines to be perpendicular? Explain and draw a pair of perpendicular lines.
3. (a) Measure the labeled angles in the diagram below and record their values.
mÐ1 = ______
mÐ2 = ______
mÐ3 = ______
mÐ4 = ______
mÐ5 = ______
mÐ6 = ______
mÐ7 = ______
mÐ8 = ______
(b) What do you notice about lines A & B?
(c) List ALL the angles that have the SAME measure as Ð1. (There should be 3).
(d) List ALL the angles that have the SAME measure as Ð2. (There should be 3).
(e) List three pairs of angles that form a linear pair (that is, together they form a straight line).
(f) How many degrees should the linear pairs add up to? ______
Add together your values for mÐ1 and mÐ4. ______
Do angles 1 and 4 add up to what they should? ______
In the diagram above, you should have noticed that line A & B are PARALLEL. Line T, which cuts across the parallel lines, is called a TRANSVERSAL.
4. In the diagram below, add a line T of your own that is a TRANSVERSAL crossing lines A and B. Try to make it cross at a DIFFERENT angle than the transversal in problem 3. Label the angles formed with the numbers 1 through 8 JUST LIKE THE DIAGRAM FOR #3. Then measure all of your angles and fill in the values below.
Add your own transversal to this diagram:
mÐ1 = ______
mÐ2 = ______
mÐ3 = ______
mÐ4 = ______
mÐ5 = ______
mÐ6 = ______
mÐ7 = ______
mÐ8 = ______
(a) What do you notice about lines A & B?
(b) List ALL the angles that have the SAME measure as Ð1. (There should be 3).
(c) List ALL the angles that have the SAME measure as Ð2. (There should be 3).
5. (a) Which pair of lines are parallel in the diagram shown below?______
(b) Which line is the TRANSVERSAL in the diagram below? ______
(c) Measure the angles in the diagram and fill in the blanks:
mÐ1 = ______
mÐ2 = ______
mÐ3 = ______
mÐ4 = ______
mÐ5 = ______
mÐ6 = ______
mÐ7 = ______
mÐ8 = ______
(d) Do the angles in this diagram follow the same pattern as in #3 and 4? Explain.
6. Look at the diagram at right. Use the patterns you found in 3, 4, and 5 above to answer the questions about this new diagram.
(a) Which pair of lines are parallel in the diagram? ______
(b) Which line is the TRANSVERSAL in the diagram? ______
(c) Which angles will have the SAME measure as Ð5? ______
(d) Which angles will have the SAME measure as Ð6? ______
(e) Suppose mÐ5 is 70º. Fill in the measurements of all of the other angles. (Don’t measure, use the patterns.)
mÐ6 = ______mÐ7 = ______mÐ8 = ______
mÐ9 = ______mÐ10 = ______mÐ11 = ______mÐ12 = ______
(f) Suppose mÐ11 is 130º. Fill in the measurements of all of the other angles. (Don’t measure with a protractor, use the patterns.)
mÐ5 = ______mÐ6 = ______mÐ7 = ______
mÐ8 = ______mÐ9 = ______mÐ10 = ______mÐ12 = ______
(g) List three pairs of supplementary angles from the diagram.
(h) List three pairs of vertical angles from the diagram.
7. Use the diagram at right. Notice that the angle marked is 122°.
(a)
(b)
(c)
(d)
8. Use the diagram at right. Notice that the angle marked is 63°
(a)
(b)
(c)
(d)
9. Look at the diagram shown at right.
(a) Which of the following equations will be a true equation that you matches the diagram? (Circle one)
2x + 8 + 3x – 13 = 90
2x + 8 + 3x – 13 = 180
2x + 8 = 3x – 13
(b) Solve the equation you chose and find the value of x.
10. Look at the diagram shown below.
(a) Which of the following equations will be a true equation that matches the diagram? (Circle one)
3x + 20 + 5x + 72 = 90
3x + 20 + 5x + 72 = 180
3x + 20 = 5x + 72
(b) Solve the equation you chose and find the value of x.
U3 WS #1 KGW 2