Unit 1B – Equations of Parallel and Perpendicular Lines (Notes)

Name Date

I can… Essential Question(s):

Key Concepts Notes Slope Definition Formula Y-Intercept Definition Slope-Intercept Form Types of Slopes: Positive Negative Zero Undefined

Refresher: How to graph lines in slope intercept form: Steps Examples:

1.

2.

3.

4.

Parallel Lines Examples: Write an equation that satisfies each condition:

a. Contains Q(-2,-4) and is parallel to

with K(2, 7) and L (2, -12)

b. Contains A(-1, -3) and is parallel to

with C(-1, 7) and D(5, 1)

Perpendicular Examples Write an equation that satisfies each condition:

a. Contains M(4, 1) and perpendicular to

with G (0, 3) and H (-3, 0)

b. Contains W(6, 4) and perpendicular to

with D (0, 2) and H (5, 0)

Addition Examples:

Determine whether and are parallel, perpendicular, or neither.

a. A(-2, -5) B(4, 7) C(0, 2) D(8, -2)

b. A(-8, -7) B(4, -4) C(-2, -5) D(1, 7)

c. A(4, 2) B(6, -3) C(-1, 5) D(-3, 10)

Summary, Reflection, Analysis…

Addition Example: Given points Q, R, S, and T, tell

which sides, if any, of quadrilateral QRST in the Figure are parallel or perpendicular.

If , find the other three

angles and explain why.

Unit 1B Section 3: Equations of Parallel and Perpendicular Lines

Name: __________________ Exercise #1

Directions: Determine whether and are parallel, perpendicular, or neither.

1. A(3, -1) B(6, 1) C(-2, -2) D(2, 4)

2. A(-3, -11) B(3, 13) C(0, -6) D(8, -8)

3. A(15, -9) B(9, -9) C(-4, -1) D(3, -1)

4. A(-3, -2) B(9, 1) C(3, 6) D(5, -2)

5. A(1, 1) B(9, 8) C(-6, 1) D(2, 8)

Directions: Write an equation of a line that satisfies each condition.

6. Contains A(6, 4), perpendicular to with M(5, 0) and N (1, 2)

7. Contains R(-4, 2), parallel to with P(0, -3) and Q(4, -2)

Directions: Graph the following conditions on the graph provided and answer the questions.

a. Graph such that A(-2, 4) and B(2, -2)

b. Graph a line that is parallel to and contains C(2, 4)

c. Graph a line that is perpendicular to and contains D(-3, -1).

d. Graph

e. The four lines all intersect to form a quadrilateral. If one of the angles of the quadrilateral is , state the other three angles and explain your reasoning.

Unit 1B Section 3: Equations of Parallel and Perpendicular Lines

Name: __________________ Exercise #2

1. Given points A, B, C, and D of quadrilateral ABCD in the Figure below, answer the following questions:

1a) State which sides, if any, of quadrilateral QRST in the Figure are parallel or

perpendicular.

1b) If and , solve for and state a reason for the equation.

2. Directions: Graph the following conditions on the graph provided and answer the questions.

a. Graph such that A(1, -6) and B(-2, 3)

b. Graph a line that is parallel to and contains C(2, 1)

c. Graph a line that is perpendicular to and contains D(3, 8). d. Graph

Questions: Answer the following:

1. Write the equation in slope-intercept form for all the above lines.

2. The four lines all intersect to form a quadrilateral. If one of the angles of the quadrilateral is , state the other three angles and explain your reasoning.

3. Directions: Graph the following conditions on the graph provided and answer the questions.

a. Graph such that A(0, 0) and B(6, 4)

b. Graph a line that is parallel to and contains C(-6, -2)

c. Graph a line that is perpendicular to and contains D(-2, 6).

Questions: Answer the following:

1. Write the equation in slope-intercept form for all the above lines.

2. The three lines intersect and form eight angles. State all angles and explain your reasoning’s.

4. Directions: Graph the following conditions on the graph provided and answer the questions.

a. Graph such that A(4, 8) and B(-4, 6)

b. Graph a line that is parallel to and contains C(0,-4)

c. Graph such that D(-1, 4) and E(2, -2)

d. Graph a line that is parallel to and contains F(7, -3)

Questions: Answer the following:

1. Write the equation in slope-intercept form for all the above lines.

2. The four lines all intersect to form a quadrilateral. If one of the angles of the quadrilateral is , state the other three angles and explain your reasoning.