Angle Lesson

11-1 Angles and Parallel Lines

Transversals

and Angle Pairs

Parallel Lines & Transversals

Parallel Lines

Remember, PARALLEL LINES are lines that lie in the same plane and do not intersect.

What is a transversal?

It is a line that intersects at least two other lines.

Transversal

A TRANSVERSAL is a line that intersects two or more lines at distinct points.

Multiple Choice

What type of angle is this?

• acute

• obtuse

• right

Parallel Lines & Transversals

When a TRANSVERSAL intersects PARALLEL LINES, 8 angles are formed.

These angles have special realtionships that are helpful to remember.

Multiple Choice

What is a transversal?

• A line that intersects at least two other lines.

• A line that intersects another line.

• A line parallel to another line.

• A line that is skew to another line.

Multiple Choice

Which figure shows a set of parallel lines?

• Figure 1

• Figure 2

• Figure 3

• Figure 4

Multiple Choice

What type of angle is this?

• acute

• obtuse

• right

Multiple Choice

True or False: This figure shows a picture of a transversal.

• True, the transversal goes from the top left to bottom right.

• True, the transversal goes from the top right to bottom left.

• False, this is a picture of intersecting lines.

This is an example of an transversal intersecting two lines.

The 8 angles formed by two parallel lines and a transversal create the following special angle pairs:

• Corresponding Angles

• Vertical Angles

• Consecutive Interior Angles

• Consecutive Exterior Angles

• Alternate Interior Angles

• Alternate Exterior Angles

Corresponding Angles

Just like corresponding parts of similar figures, CORRESPONDING ANGLES are in the same position on each parallel line.

These angle pairs are CONGRUENT.

Multiple Select

Which image(s) represent(s) the definition of a transversal?

Vertical Angles

VERTICAL ANGLES are pairs of opposite angles formed by intersecting lines.

These angle pairs are CONGRUENT.

Multiple Choice

What is the measure of the missing angle?

• 76

• 86

• 166

• 156

Multiple Choice

What angle corresponds to $$\angle1$$ ?

• $$\angle7$$

• $$\angle5$$

• $$\angle3$$

• $$\angle2$$

Corresponding Angles

Corresponding angles are angle that are in the same location but in different intersections.

Multiple Choice

Which angles are vertical angles?

• $$\angle5\ and\ \angle3$$

• $$\angle2\ and\ \angle4$$

• $$\angle1\ and\ \angle4$$

• $$\angle6\ and\ \angle4$$

Multiple Choice

What is an example of a pair of complementary angles?

• 13° and 45°
• 10° and 170°
• 81° and 9°
• 90° and 3°

Interior vs. Exterior

Angles in between the parallel lines are called INTERIOR ANGLES.

Angles that are outside of the parallel lines are EXTERIOR ANGLES.

Corresponding Angles

Consecutive vs. Alternate

CONSECUTIVE angles are on the SAME SIDE of the transversal.

ALTERNATE angles are on OPPOSITE SIDES of the transversal.

Consecutive Interior Angles

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

These angles are SUPPLEMENTARY ANGLES.

Multiple Select

Which images represent corresponding angles?

Consecutive Exterior Angles

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

These angles are SUPPLEMENTARY ANGLES.

Alternate Interior Angles

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

These angles are CONGRUENT.

Alternate Interior Angles

Alternate Exterior Angles

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

These angles are CONGRUENT.

We can also say that angles are CONGRUENT if they have equal measures.

Multiple Choice

∠3 and ∠6 are...

• Supplementary angles

• Vertical angles

• Corresponding angles

• Alternate interior angles

Alternate Exterior Angles

Multiple Choice

Angle B and Angle R are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

Angle C and Angle P are...

• Alternate Interior Angles

• Consecutive Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Select

Select the images that represent alternate interior angles.

Multiple Choice

Name the consecutive exterior interior angle to angle 1.

• 4

• 5

• 6

• 8

We can use the relationships of these angle pairs to find the measure of missing angles.

Multiple Select

Select the images that show alternate exterior angles.

Multiple Choice

If the  $$m\angle1\ =\ 57\degree,$$  find the measure of  $$\angle5$$ ?

• $$123\degree$$  

• $$57\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Find y.

• 50

• 130

• 180

• 45

Consecutive Interior Angles

Multiple Choice

Find the value of x.

• x = 100

• x = 47

• x = 90

• x = 133

Multiple Choice

What is the measure of ∠6?

• 55

• 155

• 45

• 135

Multiple Select

Zoom in on the picture. What angle are consecutive interior angles?

• $$\angle1\ and\ \angle4$$

• $$\angle3\ and\ \angle5$$

• $$\angle7\ and\ \angle8$$

• $$\angle4\ and\ \angle6$$

Multiple Choice

What is the measure of ∠1?

• 55

• 155

• 135

• 45

Multiple Choice

What is the measure of $$\ \angle A$$  ?

• 82°

• 98°

• 180°

• 8°

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle2.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Sometimes we have to use our knowledge of solving equations to help us solve problems.

Just use the relationships between the angle pairs to write an equation, then solve.

Multiple Choice

If the  $$m\angle5\ =\ 63\degree,$$  find the measure of  $$\angle3.$$  

• $$63\degree$$  

• $$117\degree$$  

• $$180\degree$$  

• Cannot be determined

Step 1: Identify the type of angle & relationship

Multiple Choice

If angle P measures 60 degrees, what is the measure of angle C?

• 60 degrees

• 30 degrees

• 120 degrees

Step 2: Write the equation to solve.

Multiple Choice

Which of the following angles would NOT be congruent to the measure of $$\angle7$$ ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle8$$  

Step 3: Solve the equation

Step 4: Check your answer

Don't forget that you can plug your answer back into the original figure/equation to check if it is correct.

Multiple Choice

Which is the correct equation to solve for x?

• $$2x-10=4x+16$$
  

• $$\left(2x-10\right)+\left(4x+16\right)=180$$
  

• $$\left(2x-10\right)+\left(4x+16\right)=90$$

Multiple Choice

Now, find the value of x.

• 13

• -3

• 29

• -13

Multiple Choice

Which of the following equations can be used to find the value of x?

• $$\left(x+16\right)+\left(4x-5\right)=90$$

• $$x+16=4x-5$$

• $$\left(x+16\right)+\left(4x-5\right)=180$$

Multiple Choice

Now solve for the value of x?

• 7

• $$3\ \frac{2}{3}$$  
  

• 33.8

• 15.8

Multiple Choice

Which equation can be used to solve for x?

• $$\left(3x\right)+\left(4x+19\right)=90$$
  

• $$\left(3x\right)+\left(4x+19\right)=180$$

• $$3x=4x+19$$
  

Multiple Choice

What is the value of x?

• 22

• 26

• 24

• 23

Multiple Choice

Which is the correct equation to solve for x?

• $$5x-8=3x+32$$

• $$\left(5x-8\right)+\left(3x+32\right)=90$$

• $$\left(5x-8\right)+\left(3x+32\right)=180$$

Multiple Choice

Now, what is the value of x?

• 20

• 19.5

• 5

• 8.25