warm up complete each sentence. 1. angles whose measures have a sum of 90° are _______________
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7-2. Parallel and Perpendicular Lines. Course 3. Warm Up Complete 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 ______________. - PowerPoint PPT PresentationTRANSCRIPT
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. A part of a line between two points is called a ____________.
Course 3
7-2 Parallel and Perpendicular Lines
complementary
congruent
supplementary
segment
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?
Course 3
7-2 Parallel and Perpendicular Lines
Odd: An odd number can only be the product of two odd numbers.
Learn to identify parallel and perpendicular lines and the angles formed by a transversal.
Course 3
7-2 Parallel and Perpendicular Lines
Vocabularyparallel lines
perpendicular lines
transversal
Insert Lesson Title Here
Course 3
7-2 Parallel and Perpendicular Lines
Course 3
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.
Course 3
7-2 Parallel and Perpendicular Lines
The railroad ties are transversals to the tracks.
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 tracks are parallel.
Course 3
7-2 Parallel and Perpendicular Lines
You cannot tell for certain if angles are congruent by measuring because measurement is not exact.
Caution!
Course 3
7-2 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°.
2, 4, 6, and 8 all measure 30°.
Course 3
7-2 Parallel and Perpendicular Lines
Additional 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 3 5 7
2 4 6 8
13
57
24
68
Course 3
7-2 Parallel and Perpendicular Lines
Check 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°.
2, 3, 6, and 7 all measure 144°.
1 23 4
5 67 8
Course 3
7-2 Parallel and Perpendicular Lines
Check 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 8
2 3 6 72
36
7
14
58
Course 3
7-2 Parallel and Perpendicular Lines
If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.
Course 3
7-2 Parallel and Perpendicular Lines
PROPERTIES OF TRANSVERSALS PROPERTIES OF TRANSVERSALS TO PARALLEL LINES TO PARALLEL LINES
If two parallel lines are intersected by a transversal, • the acute angles that are formed are all congruent,• the obtuse angles are all congruent,• and any acute angle is supplementary to any obtuse angle.If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles.
Course 3
7-2 Parallel and Perpendicular Lines
The symbol for parallel is ||. The symbol for perpendicular is .
Writing Math
In the figure, line l || line m. Find the measure of the angle.
Course 3
7-2 Parallel and Perpendicular Lines
Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals
4
m4 = 124°
All obtuse angles in the figure are congruent.
Course 3
7-2 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 the angle 124°.
m2 = 56°–124° –124°
In the figure, line l || line m. Find the measure of the angle.
Course 3
7-2 Parallel and Perpendicular Lines
Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
All acute angles in the figure are congruent.6
m6 = 56°
In the figure, line l || line m. Find the measure of the angle.
In the figure, line n || line m. Find the measure of the angle.
Course 3
7-2 Parallel and Perpendicular Lines
Check It Out: Example 2A
7
m7 = 144°
All obtuse angles in the figure are congruent
1 144°3 4
5 67 8
m
n
Course 3
7-2 Parallel and Perpendicular Lines
5
m5 + 144° = 180°
5 is supplementary to the angle 144°.
m5 = 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
Course 3
7-2 Parallel and Perpendicular Lines
All acute angles in the figure are congruent1
m1 = 36°1 144°
3 45 6
7 8
m
n
In the figure, line n || line m. Find the measure of the angle.
Check It Out: Example 2C
Course 3
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. If m5 = 120° what is m2?
1, 5, 7
1, 3, 5, 7
105°
60°