Download Unit 2: Parallel and Perpendicular Lines Rank Yourself

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
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
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.
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.
2
1
Entry
Ranking:
Date
Level
Notes: (what you didn’t understand from the chapter and want to work on)
Rank Yourself:
1
Notes
Level 4
Given that the figure is a parallelogram find the value of
a.
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)
Level 3
4. Are the two lines parallel, perpendicular, or neither?
1. Given: a b , c d
Prove: 1 and 4 are supplementary.
2. Given:
Prove:
Level 2
3. Find the value of x, y, and z:
Find the value of each angle and justify why you know that, that is the value:
Level 1
Find the value of x and y:
Entry
2
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:
Which segments are skew to
Answers
?
What are two pairs of parallel planes?
What are two segments parallel to plane RUYV?
3
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.
4
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…
5
Notes
Each of the previous has a corresponding theorem or postulate that we will use frequently.
3.2: Properties of Parallel Lines
6
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
7
Reason
Notes
Your turn:
Given:
Prove:
Statement
Reason
3-3: Converse of Parallel Lines Theorems
We will use Patty Paper to discovery something about lines:
8
Notes
Example: What value of the variable will make
Your turn:
the lines parallel?
9
Notes
Example: Proving lines
are parallel
Statement
Reason
3-6 Constructing Parallel and Perpendicular Lines
Constructing perpendicular line:
Steps:
Patty Paper
Steps
Hand Construction:
10
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?
11
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.
Draw
through B, parallel to
Given
PBC and 3 are supplementary
m PBC + m 3 = 180
Angles that form a linear pair are
Supplementary
m 1 = m A and m 3 = m C
Congruent angles have equal
measure.
Definition of suppl.
angles.
1
A and 3
C
If lines are then alt. int.
m PBC = m 1 + m 2
Angle addition post
m 1 + m 2 + m 3 = 180
Substitution property
angles are congruent
m A + m 2 + m C = 180
Substitution
Example:
property
Using the
triangle sum theorem:
Find the value of x, y, and z.
Your turn:
12
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?
13
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)
14
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?
15
Notes