Angle Relationships and Transversals

Geometry,

Section 3-1

Parallel Lines and Transversals

Objectives

• Students will be able to identify the relationship between two lines or two planes.

• Students will be able to name angles formed by a pair of lines and a transversal.

• G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line, and distance around a circular arc.

Angle Relations

• Please copy the diagram on the right.

• You will be given a name of an ANGLE RELATIONSHIP.

• Consider the meaning of the name of the ANGLE RELATIONSHIP.

• Try to determine what angles fit the ANGLE RELATIONSHIP.

​Linear Pairs

Two angles that form a line. The measure of both angles will add up to 180 degrees, making them supplementary. ​

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Adjacent Angles​

Two angles that share a VERTEX and a SIDE

(side by side) .

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Supplementary Angles​

When two or more angles have a sum of 180 degrees, making a straight line. ​

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Multiple Choice

Using your knowledge of Supplementary Angles, determine the missing angle measure.

• 122 degrees

• 118 degrees

• 28 degrees

• 32 degrees

Complementary Angles​

When two or more angles have a sum of 90 degrees, making a right angle. ​

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Multiple Choice

Using your knowledge of Complementary Angles, determine the missing angle measure.

• 70 degrees

• 72 degrees

• 58 degrees

• 66 degrees

Alternate Interior Angles

Vertical Angles​

Angles that are OPPOSITE of each other when two lines intersect.

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Vertical angles are CONGRUENT. ​

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Multiple Choice

Choose the pair of vertical angles on the diagram shown.

• angles 1 and 6

• angles 2 and 3

• angles 1 and 8

• angles 7 and 2

Open Ended

What do you think "Interior Angles" might mean?

Multiple Choice

Which angles do you think are "Interior Angles"?

• 
  

  $$\angle1,\ \angle2,\ \angle3\ and\ \angle4$$
  

• $$\angle5,\ \angle6,\ \angle7\ and\ \angle8$$

• $$\angle1,\ \angle3,\ \angle6\ and\ \angle8$$

• $$\angle2,\ \angle4,\ \angle5\ and\ \angle7$$

Open Ended

What do you think EXTERIOR ANGLES might mean?

Multiple Choice

Which angles do you think are "Exterior Angles"?

• 
  

  $$\angle1,\ \angle2,\ \angle3\ and\ \angle4$$
  

• $$\angle5,\ \angle6,\ \angle7\ and\ \angle8$$

• $$\angle1,\ \angle3,\ \angle6\ and\ \angle8$$

• $$\angle2,\ \angle4,\ \angle5\ and\ \angle7$$

Open Ended

Now that we have discussed Interior Angles, what might it mean to be ALTERNATE INTERIOR ANGLES?

Multiple Select

Which angles do you think are "Alternate Interior Angles"?

• 
  

  $$\angle2\ and\ \angle7$$
  

• $$\angle4\ and\ \angle5$$

• $$\angle2\ and\ \angle4$$

• $$\angle5\ and\ \angle7$$

• $$\angle1\ and\ \angle8$$  

Open Ended

Now that we have discussed Interior Angles (and Alternate Interior Angles), what might it mean to be CONSECUTIVE INTERIOR ANGLES?

Multiple Select

Which angles do you think are "Consecutive Interior Angles"?

• 
  

  $$\angle2\ and\ \angle5$$
  

• $$\angle4\ and\ \angle7$$

• $$\angle2\ and\ \angle4$$

• $$\angle5\ and\ \angle7$$

• $$\angle1\ and\ \angle6$$  

Open Ended

We have discussed Exterior Angles, what might it mean to be ALTERNATE EXTERIOR ANGLES?

Multiple Select

Which angles do you think are "Alternate Exterior Angles"?

• 
  

  $$\angle1\ and\ \angle8$$
  

• $$\angle3\ and\ \angle6$$

• $$\angle1\ and\ \angle6$$

• $$\angle3\ and\ \angle8$$

• $$\angle6\ and\ \angle8$$  

Open Ended

"Consecutive Exterior Angles" DO NOT exist!

Why do you thing that is?

Open Ended

What might it mean to be CORRESPONDING ANGLES?

Multiple Select

Which angles do you think are "Corresponding Angles"?  (Check all that apply.)

• 
  

  $$\angle1\ and\ \angle5$$
  

• $$\angle2\ and\ \angle6$$

• $$\angle3\ and\ \angle7$$

• $$\angle4\ and\ \angle8$$

• $$\angle3\ and\ \angle8$$  

Lets take a look at what happens when parallel lines are cut by a transversal... ​

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Parallel Lines Cut by a Transversal​

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Alternate Interior Angles​

Angles INSIDE the parallel lines and on OPPOSITE sides of the transversal.

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Alternate Interior angles are CONGRUENT. ​

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Alternate Exterior Angles​

Angles OUTSIDE the parallel lines and on OPPOSITE sides of the transversal.

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Alternate Exterior angles are CONGRUENT. ​

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Same - Side Interior Angles​

Angles INSIDE the parallel lines and on the SAME SIDE of the transversal.

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Same - Side Interior angles are SUPPLEMENTARY. ​

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Match

Match the following

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same-side Interior Angles

Vertical Angles

• Alternate Interior Angles

• Alternate Exterior Angles

• Corresponding Angles

• Same-side Interior Angles

• Vertical Angles

Multiple Choice

Find the value of x.

• 20
• 135
• 31
• 145

Multiple Choice

What is the measure of ∠8?

• 55
• 155
• 135
• 45

Multiple Choice

What is the measure of ∠3?

• 55
• 155
• 45
• 135

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Find the value of x if the  $$m\angle1\ =\ 11x\ -\ 9\degree$$ and the  $$m\angle5\ =\ 7x\ +9\degree$$ .

• -4.5

• 4.5

• 1

• 0

Multiple Choice

Solve for y.

• y = 55

• y = 35

• y = 70

• y = 68