Worksheet – Section 3-2 Angles and Parallel Lines
Worksheet ¨C Section 3-2 Angles and Parallel Lines
Objectives:
? Understand the parallel lines cut by a transversal theorem and it¡¯s converse
? Find angle measures using the Theorem
? Use algebra to find unknown variable and angle measures involve parallel lines and transversals
? Use Auxiliary lines to find unknown angle measures
Parallel Lines and Angle Pairs
When two parallel lines are cut by a transversal, the following
pairs of angles are congruent.
? corresponding angles
? alternate interior angles
? alternate exterior angles
Also, consecutive interior angles are supplementary.
Example:
In the figure, m¡Ï2 = 75. Find the measures of the
remaining angles.
Example:
In the figure, m¡Ï3 = 102. Find the measure of each
angle. Tell which postulate(s) or theorem(s) you used.
a. ¡Ï5
b. ¡Ï6
c. ¡Ï11
d. ¡Ï7
e. ¡Ï15
f. ¡Ï14
Practice
In the figure, m¡Ï9 = 80 and m¡Ï5 = 68. Find the measure
of each angle. Tell which postulate(s) or theorem(s) you used.
a. ¡Ï12
b. ¡Ï1
c. ¡Ï4
d. ¡Ï3
e. ¡Ï7
f. ¡Ï16
Algebra and Angle Measures
Algebra can be used to find unknown values in angles formed by a transversal and parallel lines.
Example:
If m¡Ï1 = 3x + 15, m¡Ï2 = 4x - 5, and m¡Ï3 = 5y, find the
value of x and y.
Example:
Find the value of the variable(s) in each figure.
Explain your reasoning.
Example:
Find the value of the variable(s) in each figure. Explain
your reasoning.
Example(Using a 3rd parallel Line ¨C Auxilury Line)
Practice:
Find the value of the variable(s) in each figure. Explain
your reasoning.
Practice:
Find the value of the variable(s) in each figure. Explain your
reasoning.
Homework:
In the figure, m¡Ï2 = 92 and m¡Ï12 = 74. Find the
measure of each angle. Tell which postulate(s) or
theorem(s) you used.
1. ¡Ï10
2. ¡Ï8
3. ¡Ï9
4. ¡Ï5
5. ¡Ï11
6. ¡Ï13
7. Find the value of the variable(s) in each figure.
Explain your reasoning.
8. Find the value of the variable(s) in each figure.
Explain your reasoning.
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