Angles created by transversal and paralle

Ms. Johnson 8th Grade math

Parallel lines: Lines that are the same distance apart over their entire length

Parallel lines: Lines that are the same distance apart over their entire length

Transversal: a line that crosses two other lines

When you have a transversal cutting across parallel lines certain relationships are formed

Lines l and m are parallel.l||m

120°

l

m

120°

120°

120°

Note the 4 angles that measure 120°.

nLine n is a transversal.


60°

l

m

60°

60°

60°

Note the 4 angles that measure 60°.



60°

l

m

60°

60°

60°

There are many pairs of angles that are supplementary.

There are 4 pairs of angles that are vertical.

120°

120°

120°

120°


Practice Time!

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

b°

d°

f°

a °

c°

e°

g°



42°

l

m

42°

42°

42°

138°

138°

138°

138°



81°

l

m

b°

d°

f°

a °

c°

e°

g°



81°

l

m

81°

81°

81°

99°

99°

99°

99°

So we know that given a transversal cutting 2 parallel lines, certain relationships are formed. Some of the angles are supplementary because they are on a straight line. And some angles are vertical and thus equal.

But in this picture, how did we know that the angles highlighted in red are the same????

120°

l

m

120°

120°

120°


We knew because there are angle relationships of equality besides the vertical angle theorem..

Congruent Angle Relationships (=):VerticalAlternate Interior (AI)Alternate Exterior (AE)Corresponding

We knew because there are angle relationships of equality besides the vertical angle theorem..

Congruent Angle Relationships (=):VerticalAlternate Interior (AI)Alternate Exterior (AE)Corresponding

If the angles in the scenario are not equal to each other, then they are supplementary!!

The easiest way to see these relationships: Imagine a sandwich. The parallel lines are the bread.The transversal is the toothpick.

Vertical angles: are on the same slice of “bread” on different sides of the “toothpick.”

Alternate Interior angles: are inside the “bread”, on opposite sides of the “toothpick.”

Alternate Interior angles: are inside the “bread”, on opposite sides of the “toothpick.”

Alternate Exterior angles: are outside the “bread,” on opposite sidesof the “toothpick.”

Corresponding angles: are on different slices of “bread,” on the same side of the toothpick.

Angles are in the same position (both aretop left, top right, bottom left, or bottom right). It’s almost like you put one slice of bread on top of the other.

We actually already know how to find the missing angle using algebra.

First, identify the relationship.


First, identify the relationship. Second, write the equation. If it’s any of these:

Vertical (V)Alternate exterior (AE)Alternate interior (AI)Corresponding (C)

Then use the same equation you do for all equal relationships. Angle = Angle (the sneaker)

And solve for x. Substitute if necessary.


First, identify the relationship. Second, write the equation. If it’s NOT any of these:

Vertical (V)Alternate exterior (AE)Alternate interior (AI)Corresponding (C)

Then the relationship has to be supplementary, so the equation is Angle + Angle = 180 (“the boot”)

And solve for x. Substitute if necessary.

(2x)°

120°

Find x and the unknown angle.

Use Algebra to Find Missing Angles Ex. 1

(2x)°

120°


First, we identify the relationship:

(2x)°

120°


First, we identify the relationship: Alternate Interior

(2x)°

120°


First, we identify the relationship: Alternate Interior

which means the angles are congruent (=)

(2x)°

120°


2x = 120

(2x)°

120°


2x = 1202 2

(2x)°

120°


2x = 120• 2 x = 60

(2x)°

120°


Now to find the unknown angle, we can just substitute back in.

We need to find what angle 2x equals….. 2(60) = 120So the unknown angle is 120°


Example 2

2x + 20

70°


First we identify the relationship.

Example 2

2x + 20

70°


First we identify the relationship.Corresponding

Example 2

2x + 20

70°


First we identify the relationship.CorrespondingSo angle = angle

Example 2

2x + 20

70°


Corresponding

2x + 20 = 70

Example 2

2x + 20

70°


Corresponding

2x + 20 = 70-20 -20

2x = 50

Example 2

2x + 20

70°


Corresponding

2x + 20 = 70-20 -20

2x = 502 2

Example 2

2x + 20

70°


Corresponding

2x + 20 = 70-20 -20

2x = 50• 2

x = 25

Example 2

2x + 20

70°


Now we substitute back in.

2(25) + 20 =

Example 2

2x + 20

70°


Now we substitute back in.

2(25) + 20 = 70

So the missing angle is 70°

Example 2

2x + 20

70°


Example 2

(3x + 30)°

(2x + 40)°


Example 2

(3x + 30)°

(2x + 40)°

Find the relationship.


Example 2

(3x + 30)°

(2x + 40)°

Find the relationship. Theseangles are supplementary. So angle + angle = 180


Example 2

(3x + 30)°

(2x + 40)°

Supplementary

3x + 302x + 40 = 180


Example 2

(3x + 30)°

(2x + 40)°

Supplementary

3x + 302x + 405x + 70 = 180


Example 2

(3x + 30)°

(2x + 40)°

Supplementary

3x + 302x + 405x + 70 = 180

-70 -70

5x = 110


Example 2

(3x + 30)°

(2x + 40)°

Supplementary

3x + 302x + 405x + 70 = 180

-70 -70

5x = 110• 5 x = 22


Example 2

(3x + 30)°

(2x + 40)°

Supplementary

x = 22

Now substitute into angles:

3(22) + 30 = 96

2(22) + 40 = 84

ACTIVITY

Green cards: Name the relationship. Write about how you identifiedthe relationship. Use 2-Step Equations to findx and the missing angle.

Pink cards: Name the relationship. Write about how you identifiedthe relationship. Use Multi-Step Equations to findx and the missing angles.

Angles created by transversal and paralle

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