1 Notes

Unit 2: Parallel and Perpendicular Lines

Scale for Unit 2

4 I have mastered level 3 and I can determine the angles of a parallelogram.

3 I have mastered level 2 and I can:

Identify skewed, parallel, and perpendicular lines from diagrams or on the

coordinate plane.

I can write the equation of parallel and perpendicular lines

2 I have mastered level 1 and I can:

Use the triangle angle sum theorem to find missing values

Write proofs to prove information about angles or that lines are parallel

1 I have mastered the Entry level and I can identify and know the relationship

(thm/post) between alternate interior angles, alternate exterior angles,

corresponding angles, and same-side interior angles.

Entry I can define vertical angle and know what the vertical angles theorem is. I can

define linear pair and know what the linear pair postulate is.

Ranking:

Date

Level

Rank Yourself:

Notes: (what you didn’t understand from the chapter and want to work on)

2 Notes

Level 4 Given that the figure is a parallelogram find the value of

a.

Level 3

1. Identify a line parallel to line AB

2. Identify a line that is skew to line FE

3. Write the slope intercept form of a line perpendicular to y = 3x – 5 and

passes through (4, -5)

4. Are the two lines parallel, perpendicular, or neither?

Level 2

1. Given: ,a b c d 2. Given:

Prove: 1 and 4 are supplementary. Prove:

3. Find the value of x, y, and z:

Level 1

Find the value of each angle and justify why you know that, that is the value:

Entry

Find the value of x and y:

3 Notes

3.1: Lines and Angles

Objective: Students will be able to identify relationships between figures in space and to identify

angles formed by two lines and a transversal.

Transversal: A line that ______________________two or more lines at distinct points.

Example: Which segments are parallel to ?

Your Turn: Answers

Which segments are skew to ?

What are two pairs of parallel planes?

What are two segments parallel to plane RUYV?

4 Notes

Claim it! Use on of the four diagrams below to play each round of the game. At the beginning of each

round, you and your partner must each claim an angle and label it with your initials. Take turns rolling

the number cube to determine an angle relationship.

1 = alternate interior 2 = alternate exterior 3 = corresponding

4 = same side interior 5 = vertical angles 6 = linear pair

Then initial one angle that has the given relationship to the angle you claimed. On subsequent turns, you

may start from any previously initialed angles in the angle relationship. Angles may only be claimed once,

so it may not always be possible to claim an angle on your turn.

5 Notes

3.2: Properties of Parallel Lines Geogebra Discovery

Objective: Students will be able to prove theorems about parallel lines and use properties of parallel

lines to find angle measures.

Thinking back to the angle pairs we discussed yesterday, what do you think will happen to the angle pairs

when we use parallel lines cut by a transversal? Write your thoughts below:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

When parallel lines are cut by a transversal… Rule

Alternate Interior angles are…

Alternate Exterior angles…

Same- Side Interior Angles…

Corresponding Angles…

6 Notes

Each of the previous has a corresponding theorem or postulate that we will use frequently.

3.2: Properties of Parallel Lines

7 Notes

Example: Finding missing angle measures:

Find the measure of and list what thm or post justifies your answer

Your turn: Find the measure of each and list what thm or post justifies your answer:

Example: Using Algebra to find missing angles

Find the value of x and y:

Your turn: Find the value of p:

Example: Proofs using parallel lines cut by a transversal

Given:

Prove:

Statement Reason

8 Notes

Your turn:

Given:

Prove:

Statement Reason

3-3: Converse of Parallel Lines Theorems

We will use Patty Paper to discovery something about lines:

9 Notes

Example: What value of the variable will make

the lines parallel?

Your turn:

10 Notes

Example: Proving lines

are parallel

Statement Reason

3-6 Constructing Parallel and Perpendicular Lines

Constructing perpendicular line:

Steps:

Patty Paper

Steps Hand Construction:

11 Notes

Construction of parallel lines:

Steps:

Patty Paper

Steps

Hand Construction:

3-5: Parallel Lines and Triangles

Using half of an index card cut diagonally, label the three angles of your triangle A, B and C.

Cut the triangle into three pieces so that the angles are alone.

Arrange the angles below so that all three points touch each other. What do you notice?

12 Notes

Flow Proof: Arrows show the ________________ connection between statements.

We will now use a flow proof to prove a very important theorem, the triangle sum theorem.

Given

Angles that form a linear pair are Definition of suppl. Angle addition post

Supplementary angles.

Example:

Using the

triangle sum theorem:

Find the value of x, y, and z.

Your turn:

Draw through B, parallel to

PBC and 3 are supplementary m PBC + m 3 = 180 m PBC = m 1 + m 2

m 1 + m 2 + m 3 = 180 1 A and 3 C

Substitution property

If lines are then alt. int.

angles are congruent

m 1 = m A and m 3 = m C

Congruent angles have equal

measure.

m A + m 2 + m C = 180

Substitution

property

13 Notes

Example: Using the Triangle Exterior Angle Theorem

Examples using triangle theorems: The ratio of the angle measures of the acute angles in a right

triangle is 1:2. Find the measures of the other two angles.

Your turn: The measure of one angle of a triangle is 40. The measures of the other two angles are in a

ratio of 3:4. Find the measure of the other two angles.

3-8: Equations of Parallel and Perpendicular Lines in the Coordinate Plane

Using the pictures from the bellwork what do you notice about parallel lines?

Perpendicular lines?

14 Notes

Types of slope:

Example: Find the slope between the points (2, -4) and (-1, -3)

Your turn: Find the slope between the points (1, -2) and (5, -7)

15 Notes

Example: Equations of Parallel and Perpendicular Lines

What is an equation in slope-intercept form for the line perpendicular to y=3x + 2 that contains (6, 2)

Your turn: What is an equation in point-slope form of a line parallel to y = 4x -2 that contains (-2, -2)

Are the following lines parallel, perpendicular or neither?