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9-2 Parallel and Perpendicular Lines
Warm UpWarm Up
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Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
9-2 Parallel and Perpendicular Lines
Warm UpComplete each sentence.
1. Angles whose measures have a sum of 90° are _______________ .
2. Vertical angles have equal measures, so they are ______________.
3. Angles whose measures have a sum of 180° are ______________.
4. An angle that measures less than 90° is a(n) ____________ angle.
complementary
congruent
supplementary
acute
9-2 Parallel and Perpendicular Lines
Problem of the Day
The square root of 1,813,141,561 is a whole number. Is it odd or even? How do you know?
Odd: An odd number can only be the product of two odd numbers.
9-2 Parallel and Perpendicular Lines
MA.8.G.2.2 Classify and determine the measure of angles, including angles created when parallel lines are cut by transversals.
Sunshine State Standards
9-2 Parallel and Perpendicular Lines
Vocabularyparallel lines
perpendicular lines
transversal
9-2 Parallel and Perpendicular Lines
Parallel lines are lines in a plane that never meet.
Perpendicular lines are lines that intersect at 90° angles.
9-2 Parallel and Perpendicular Lines
The sides of the windows are transversals to the top and bottom.
A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties.
The top and bottom of the windows are parallel.
9-2 Parallel and Perpendicular Lines
You cannot tell if angles are congruent by measuring because measurement is not exact.
Caution!
9-2 Parallel and Perpendicular Lines
Additional Example 1: Identifying Congruent Angles Formed by a Transversal
Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent?
1, 3, 5, and 7 all measure 150° and appear to be congruent.
2, 4, 6, and 8 all measure 30° and appear to be congruent.
9-2 Parallel and Perpendicular Lines
Additional Example 1 Continued
Angles circled in blue appear to be congruent to each other, and angles circled in red appear to be congruent to each other.
1 3 5 7
2 4 6 8
9-2 Parallel and Perpendicular Lines
Check It Out: Example 1
Measure the angles formed by the transversal and the parallel lines. Which angles appear to be congruent?
1, 4, 5, and 8 all measure 36° and appear congruent.2, 3, 6, and 7 all measure 144° and appearcongruent.
1 23 4
5 67 8
9-2 Parallel and Perpendicular Lines
Some pairs of the eight angles formed by two parallel lines and a transversal have special names.
9-2 Parallel and Perpendicular Lines
9-2 Parallel and Perpendicular Lines
The symbol for parallel is ||. The symbol for perpendicular is .
Writing Math
9-2 Parallel and Perpendicular Lines
In the figure, line l || line m. Find the measure of the angle.
Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals
4
m4 = 124°
The 124 angle and 4 are corresponding angles.
9-2 Parallel and Perpendicular Lines
Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
2
m2 + 124° = 180°
2 is supplementary to angle 124°.
m2 = 56°–124° –124°
In the figure, line l || line m. Find the measure of the angle.
9-2 Parallel and Perpendicular Lines
Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
6
m6 = 56°
In the figure, line l || line m. Find the measure of the angle.
m6 + 124° = 180°
6 is supplementary to angle 6.
m6 = 56°–124° –124°
9-2 Parallel and Perpendicular Lines
In the figure, line n || line m. Find the measure of each angle. Justify your answer.
Check It Out: Example 2A
5
36°; possible answer: 5 is congruent to 1, which is supplementary to the given angle,180° – 144° = 36°
1 144°3 4
5 67 8
m
n
9-2 Parallel and Perpendicular Lines
7
144°; possible answer: 7 and the 144° angle are alternate exterior angles, which are congruent.
1 144°3 4
5 67 8
m
n
Check It Out: Example 2B
In the figure, line n || line m. Find the measure of each angle. Justify your answer.
9-2 Parallel and Perpendicular Lines
8
36°; possible answer: 8 and 7 are supplementary angles, 180° – 144° = 36°
1 144°3 4
5 67 8
m
n
Check It Out: Example 2C
In the figure, line n || line m. Find the measure of each angle. Justify your answer.
9-2 Parallel and Perpendicular Lines
6
144°; possible answer: 6 and the 144° angle are corresponding angles, which are congruent.
1 144°3 4
5 67 8
m
n
Check It Out: Example 2D
In the figure, line n || line m. Find the measure of each angle. Justify your answer.
9-2 Parallel and Perpendicular Lines
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
9-2 Parallel and Perpendicular Lines
Lesson Quiz
In the figure, a || b.
1. Name the angles congruent to 3.
2. Name all the angles supplementary to 6.
3. If m1 = 105° what is m3?
4. What is m6?
1, 5, 7
1, 3, 5, 7
105°
75°
9-2 Parallel and Perpendicular Lines
1. In the figure, x || y. Identify the angles congruent to 3.
A. 1, 2, 4
B. 2, 4, 6
C. 4, 5, 6
D. 1, 5, 8
Lesson Quiz for Student Response Systems
9-2 Parallel and Perpendicular Lines
2. In the figure, x || y. If m5 = 115°, what is m7?
A. 25°
B. 65°
C. 75°
D. 115°
Lesson Quiz for Student Response Systems