Math 10-3

Unit 5 Angles and Parallel Lines

Lesson 54 Parallel Lines and Transversals

Formula page

I expect that you will be able to use a formula page for this class,  but that will be determined by your teacher.

Your teacher may have a formula page they expect you to use.

Below is a link to the formula page I will use (at least for now!) when I’m doing questions for this class.

This may change, depending on feedback from your teacher.

I encourage you to download this page and print it so you have it handy when you are doing math.

LINK
https://drive.google.com/open?id=1EMauePx-P6WrtTIcd7-AtNnmJt8zqXpI

Explore the Math Pages 209 - 212

Read/Work through this section of your textbook.
These ideas will be developed in the examples

Your teacher will let you know which pages you need to do for this lesson.

In this lesson, we discuss EXACTLY THE SAME IDEAS as the previous lesson, except now, we look at the SPECIAL CASE where we have two PARALLEL lines and a transversal.

I covered this special case in the previous lesson.

NOTE!!!   The HINT on page 210 is wrong!
If the corresponding angles are equal, the lines ARE parallel!

Example 1  Pages 212 - 213

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Example 2  Page 213

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Build Your Skills Pages 214 - 217

These questions all come from your textbook.

If you need extra practice or want to maintain your skills,  see the NEXT section for more practice questions.

Doing Practice Problems

The problems in this section reinforce the math presented in this lesson, and give you opportunities to build on and practice your skills.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

•	EXTEND YOUR THINKING problems will be more challenging than the others.

Notes

Question 8,    I didn’t do a video for this one.
Mirrors can be very tricky.
Check the answer in the back if you are interested in this one.
Right angle mirrors   LINK
Another link   LINK

Below, an illustration of the effect.  
Notice the words are reverse orientation in the one mirror,  but CORRECT in the mirror on the right.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7",  , , }})

Develop and Maintain Your Skills

Doing these problems

These questions are provided to help you develop and maintain your skills with the ideas of this lesson.

These questions are modelled after the questions in the textbook,  so there is nothing different here, just more questions if you need them.

These questions are completely optional (unless your teacher specifically assigns them)

Each question has an answer AND a video solution.

DO your best to answer the question YOURSELF first!

Check your work with the answer provided.

If you make a mistake,  try to fix it!

Use the video solutions for more information.

If a problem still doesn't make sense, ASK YOUR TEACHER FOR HELP!

Practice Problems

Problem

Consider the diagram below, in which (Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 2])  . 
What are the measures of the three indicated angles? 
Explain how you reached your answers.

Answer

Angle 1,  122 °
Angle 2, 58°
Angle 3, 58°

Video Solution Link

Problem

In the diagram below, (Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 2]). 
State the measures of the indicated angles and explain your reasoning.

Answer

Angle 1,  109 °
Angle 2, 62°
Angle 3, 118°
Angle 4, 62°

Video Solution Link

Problem

What are the measures of the interior angles in the trapezoid shown below? (Hint:

Be careful of the order in which you calculate the angles.)

Answer

Angle 1,  112 °
Angle 2, 68°
Angle 3, 68°
Angle 4, 112°

Video Solution Link

Problem

Quadrilateral ABCD is a parallelogram in which ∠B measures 74°. 
Determine the measures of the other angles and state your reasons.

Answer

Angle A,  106°
Angle C, 106°
Angle D, 74°

Video Solution Link

Problem

Given the diagram below, identify all the pairs of parallel lines and explain your selection.

Answer

(Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 2])
(Subscript[ℓ, 4])  is parallel to  (Subscript[ℓ, 6])

Video Solution Link

Problem

Find a pair of parallel lines in the following diagram. 
On the diagram, mark all the angles necessary to determine this.

Answer

(Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 3])

Video Solution Link

Problem

What size must ∠1 be if (Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 2])?
(the second line should be labelled (Subscript[ℓ, 2]))

Answer

Angle 1 must measure 57°

Video Solution Link

Problem

The two vertical pipes in the diagram need to be moved to be parallel to each other.

By what angle must the plumber move the second pipe?

Answer

Move the second pipe 4° (away from the first pipe)

Video Solution Link

Problem

Given parallelogram ABCD, determine the values of ∠B, ∠C, and ∠D in that order, stating your reason for each measure.

Answer

Angle B,  50°
Angle C, 130°
Angle D, 50°

Video Solution Link

Problem

If (Subscript[ℓ, 1])  is parallel to  (Subscript[ℓ, 2])  and are intersected by transversals t and (Subscript[t, 2]), what are the measures of the indicated angles? 
Solve for the measures in the given order, stating your reasoning.

Answer

Angle 1,  54°
Angle 2, 54°
Angle 3, 97°
Angle 4, 83°

Video Solution Link

Problem

In the diagram below, if the side of the house and the side of the shed are parallel, what are the measures of ∠1 and ∠2?

Answer

Angle 1,  122°
Angle 2, 90°

Video Solution Link

Problem

A plumber must install pipe 2 parallel to pipe 1. He knows that ∠1 is 53°. What is the measure of ∠2?

Answer

Angle 2, 127°

Video Solution Link