PARALLEL AND
PERPENDICULAR
LINES
Essential Question: How can you tell if two
lines are parallel or perpendicular?
Demonstrated in writing in the summary at
the end of the notes.
Parallel Lines
• In a coordinate plane, two nonvertical lines
are parallel if and only if they have the
same slope.
• Any two vertical lines are parallel.
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Proof that Parallel lines have equal slopes.
• Given: line m and n are nonvertical lines, m||n, 𝐴𝐶 ≅ 𝐷𝐹
• Prove: the slopes of lines m and n are the same
Statement
Reason
1. Lines m and n are nonvertical
lines
2. m || n
3.
4. ∠C ≅∠F
5. ∠BAC ≅ ∠ EDF
6. Δ ABC ≅ Δ DEF
7. 𝐵𝐶 ≅ 𝐸𝐹
1. Given
8.
𝐵𝐶
𝐴𝐶
2.
3.
4.
5.
6.
7.
8.
9.
=
9. The slopes of lines m and n
are theQuestion:
same How can you tell if two lines are parallel or perpendicular?
Essential
Demonstrated in writing in the summary at the end of the notes.
Perpendicular Lines
• In a coordinate plane, two nonvertical
lines are perpendicular if and only if
the product of their slopes is -1.
• Horizontal lines are perpendicular to
vertical lines.
• If two lines are perpendicular to one
another the slopes will be opposite
reciprocals of one another.
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Example: Determine if the two lines are
parallel, perpendicular, or neither.
• y = 3x + 5
• 2x – 3y = 6
• y = 1/3 x – 6
• -3x +2y = -10
•y=½x–3
• -5x + 3y = 12
• y = -2x + 4
• 5x – 3y = 21
• y = 4x + 17
• 3x + 3y = 6
• y = 4x – 3
• -1/2 x + y = 7
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Remember: To write the equation of a line
• If you are given the slope and the y-intercept:
• use y = mx + b
• m is the slope
• b is the y-intercept
• If you are given the slope and one point:
• Use y - y1 = m(x – x1)
• m is the slope
• The coordinates of the point you are given are (x1, y1)
• If you are given two points:
• Calculate the slope using 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
• Then use the slope and either of the points with the equation
y - y1 = m(x – x1)
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Example: Find the slope of each line.
Which lines are parallel?
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Example: Line h passes through the points (3, 0) and (7, 6).
Graph the line perpendicular to h that passes through the
point (2, 5).
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.
Example: Write the equation of the line parallel
to the line y = -2x +3 that passes through (1, -4).
Essential Question: How can you tell if two lines are parallel or perpendicular?
Demonstrated in writing in the summary at the end of the notes.