7-2 parallel and perpendicular lines warm up complete each sentence. 1. angles whose measures have a...
DESCRIPTION
7-2 Parallel and Perpendicular Lines Vocabulary parallel lines perpendicular lines transversalTRANSCRIPT
7-2 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
7-2 Parallel and Perpendicular Lines
Learn to identify parallel and perpendicular lines and the angles formed by a transversal.
7-2 Parallel and Perpendicular Lines
Vocabularyparallel linesperpendicular linestransversal
7-2 Parallel and Perpendicular Lines
Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks.
Perpendicular lines are lines that intersect at 90° angles.
7-2 Parallel and Perpendicular Lines
You cannot tell if angles are congruent by measuring because measurement is not exact.
Caution!
7-2 Parallel and Perpendicular LinesAdditional Example 1: Identifying Congruent Angles
Formed by a TransversalMeasure 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.
7-2 Parallel and Perpendicular LinesAdditional 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 72 4 6 8
7-2 Parallel and Perpendicular LinesCheck It Out: Example 1
Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent?
1, 4, 5, and 8 all measure 36° and appear to be congruent.2, 3, 6, and 7 all measure 144° and appear to be congruent.
1 23 4
5 67 8
7-2 Parallel and Perpendicular LinesCheck It Out: Example 1 Continued
Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other.
1 4 5 82 3 6 7
23
67
14
58
7-2 Parallel and Perpendicular Lines
Some pairs of the eight angles formed by two parallel lines and a transversal have special names.
7-2 Parallel and Perpendicular Lines
7-2 Parallel and Perpendicular Lines
The symbol for parallel is ||. The symbol for perpendicular is .
Writing Math
7-2 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.
7-2 Parallel and Perpendicular LinesAdditional 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.
7-2 Parallel and Perpendicular LinesAdditional 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°
7-2 Parallel and Perpendicular Lines
In the figure, line n || line m. Find the measure of the angle.
Check It Out: Example 2A
7
m7 = 144°
The 144 angle and 7 are alternate exterior angles.
1 144°3 4
5 67 8
m
n
7-2 Parallel and Perpendicular Lines
1
m1 + 144° = 180°
1 is supplementary to the 144° angle.
m1 = 36°–144° –144°
1 144°3 4
5 67 8
m
n
In the figure, line n || line m. Find the measure of the angle.
Check It Out: Example 2B
7-2 Parallel and Perpendicular Lines
5 and 1 are corresponding angles.5
m5 = 36° 1 144°3 4
5 67 8
m
n
In the figure, line n || line m. Find the measure of the angle.
Check It Out: Example 2C
7-2 Parallel and Perpendicular Lines
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
7-2 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°
7-2 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
7-2 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