Discovering Properties of Parallel Lines
During this lesson, you will discover properties of parallel lines.
Recall: Two or more lines are parallel if and only if
_______________________________________________________.
Angle Measure Angle Measure
1
5
2
6
3
7
4
8
1
3
2
4
5 6
7 8
Investigation: Using the lines on a piece of lined or graph paper as a guide,
draw a pair of parallel lines. If you don’t have ruled paper, use both sides of
a ruler or straightedge to carefully draw parallel lines. Label the angles with
numbers as in the diagram above.
Do you notice a pattern between the measures of corresponding angles,
alternate interior angles, or alternate exterior angles? Use your
investigations to state at least three conjectures:
Conjecture: If two parallel lines are cut by a transversal, then the
corresponding angles are ______________________________________.
Conversely, ________________________________________________.
Conjecture: If two parallel lines are cut by a transversal, then the alternate
interior angles are __________________________________________.
Conversely, ________________________________________________.
Conjecture: If two parallel lines are cut by a transversal, then the alternate
exterior angles are __________________________________________.
Conversely, ________________________________________________.
Mrs. McConaughy Geometry
Discovering Properties of Parallel Lines
Conjecture: If two parallel lines are cut by a transversal, then the sameside interior angles are _____________________________________.
Conversely, ________________________________________________.
FINAL CHECKS FOR UNDERSTANDING:
1
5
10
9
13
14
2
6
3
11
15
c
7
12
4
a
8
b
16
d
1. a. Using the figure above, name all angles which are congruent to angle 4 , given a // b.
_____ _____ _____
b. Using the figure above, name all angles which are congruent to angle 16 , given c // d.
_____ _____ _____
c. Using the figure above, name all angles which are congruent to angle 1, given a // b and c
// d.
_____ _____ _____
2
100 1
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
HOMEWORK ASSIGNMENT: Discovering Properties of Parallel Lines WS 1,
2, 6, and 7. Textbook, pages 118-119: 1-7 all, 11-17 all, 23, 25.
Mrs. McConaughy Geometry