pre-algebra 5-2 parallel and perpendicular lines 5-2 parallel and perpendicular lines pre-algebra...
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Pre-Algebra
5-2 Parallel and Perpendicular Lines5-2 Parallel and Perpendicular Lines
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
5-2 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. A part of a line between two points is called a ____________.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
complementary
congruent
supplementary
segment
Pre-Algebra
5-2 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?
An odd number can only be the product of two odd numbers. Since 1,813,141,561 is an odd number, its square root is also an odd number.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Learn to identify parallel and perpendicular lines and the angles formed by a transversal.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Vocabularyparallel lines
perpendicular lines
transversal
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Parallel lines are two lines in a plane that never meet, like a set of perfectly straight, infinite train tracks.
Perpendicular lines are lines that intersect to form 90° angles.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
The railroad ties are transversals to the tracks.
A transversal is a line that intersects any two or more other lines. Transversals to parallel lines have interesting properties.
The tracks are parallel.
Pre-Algebra
5-2 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°.
Pre-Algebra
5-2 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 72 4 6 8
13
57
24
68
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Try This 1: 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
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Try This 1: 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 2
36
7
14
58
Pre-Algebra
5-2 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.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
The symbol for parallel is ||. The symbol for perpendicular is .
Writing Math
Pre-Algebra
5-2 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
A. 4
m4 = 124°
All obtuse angles in the figure are congruent.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued
B. 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.
Pre-Algebra
5-2 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.C. 6
m6 = 56°
In the figure, line l || line m. Find the measure of the angle.
Pre-Algebra
5-2 Parallel and Perpendicular Lines
In the figure, line n || line m. Find the measure of the angle.
Try This: Example 2A
A. 7
m7 = 144°
All obtuse angles in the figure are congruent
1 144°3 4
5 67 8
m
n
Pre-Algebra
5-2 Parallel and Perpendicular Lines
B. 5
m2 + 144° = 180°
5 is supplementary to the angle 144°.
m2 = 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.
Try This: Example 2B
Pre-Algebra
5-2 Parallel and Perpendicular Lines
All obtuse angles in the figure are congruentC. 6
m6 = 144°1 144°
3 45 6
7 8
m
n
In the figure, line n || line m. Find the measure of the angle.
Try This: Example 2C
Pre-Algebra
5-2 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.
Pre-Algebra
5-2 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°