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Angles and Parallel Lines. Lesson 2-4. Transversal. Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m , eight angles of the following types are formed: Exterior angles

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Angles and parallel lines l.jpg

Angles and Parallel Lines

Lesson 2-4

Lesson 2-4: Angles and Parallel Lines


Transversal l.jpg
Transversal

  • Definition: A line that intersects two or more lines in a plane at different points is called a transversal.

  • When a transversal t intersects line n and m, eight angles of the following types are formed:

    Exterior angles

    Interior angles

    Consecutive interior angles

    Alternative exterior angles

    Alternative interior angles

    Corresponding angles

t

m

n

Lesson 2-4: Angles and Parallel Lines


Vertical angles linear pair l.jpg
Vertical Angles & Linear Pair

Two angles that are opposite angles. Vertical angles are congruent.

Vertical Angles:

Linear Pair:

1  4, 2  3, 5  8, 6  7

Supplementary angles that form a line (sum = 180)

1 & 2 ,2 & 4 , 4 &3, 3 & 1,

5 & 6,6 & 8, 8 & 7, 7 & 5

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Lesson 2-4: Angles and Parallel Lines


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Angles and Parallel Lines

  • If two parallel lines are cut by a transversal, then the following pairs of angles are congruent.

  • Corresponding angles

  • Alternate interior angles

  • Alternate exterior angles

  • If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary.

  • Consecutive interior angles

  • Consecutive exterior angles

Continued…..

Lesson 2-4: Angles and Parallel Lines


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Corresponding Angles & Consecutive Angles

Corresponding Angles: Two angles that occupy corresponding positions.

 2  6, 1  5,3  7,4  8

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2

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Lesson 2-4: Angles and Parallel Lines


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Consecutive Angles

Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal.

Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal.

m3 +m5 = 180º, m4 +m6 = 180º

1

2

m1 +m7 = 180º, m2 +m8 = 180º

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8

Lesson 2-4: Angles and Parallel Lines


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Alternate Angles

  • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair).

  • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.

3  6,4  5

2  7,1  8

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Lesson 2-4: Angles and Parallel Lines


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B

A

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Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers.

m<2=80° m<3=100° m<4=80°

m<5=100° m<6=80° m<7=100° m<8=80°

m<9=100° m<10=80° m<11=100° m<12=80°

m<13=100° m<14=80° m<15=100° m<16=80°

Lesson 2-4: Angles and Parallel Lines


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B

A

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s

t

Example:

If line AB is parallel to line CD and s is parallel to t, find:

1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.

2. the value of x, if m<1 = 100 and m<8 = 2x + 10.

3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.

ANSWERS:

1. 30

2. 35

3. 33

Lesson 2-4: Angles and Parallel Lines