Mathematics
Grade 7
15 min
Parallel, perpendicular, and intersecting lines
Parallel, perpendicular, and intersecting lines
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1
Introduction & Learning Objectives
Learning Objectives
Define parallel, perpendicular, and intersecting lines.
Identify the relationship between two lines in a diagram as parallel, perpendicular, or intersecting.
Describe the relationship between the slopes of parallel lines.
Describe the relationship between the slopes of perpendicular lines.
Use the properties of intersecting lines to find the measures of unknown angles.
Draw examples of each type of line relationship.
Recognize examples of parallel, perpendicular, and intersecting lines in real-world scenarios.
Have you ever noticed how the streets in a city grid cross each other, while railroad tracks run alongside each other but never touch? 🗺️
In this lesson, we will explore three important ways lines can relate to each other: they can be parallel, p...
2
Key Concepts & Vocabulary
TermDefinitionExample
Intersecting LinesTwo or more lines that cross each other at exactly one point.The two lines that form the letter 'X' are intersecting lines.
Parallel LinesTwo lines on the same plane that are always the same distance apart and never intersect, no matter how far they are extended.The two rails of a straight train track are parallel.
Perpendicular LinesTwo lines that intersect to form a perfect right angle (90°). This is a special type of intersecting line.The corner of a square or the intersection of a wall and the floor are perpendicular.
SlopeA number that measures the steepness of a line. It's often described as 'rise over run'.A line that goes up 2 units for every 1 unit it goes to the right has a slope of 2/1 or 2.
Right AngleAn angle th...
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Core Formulas
Rule for Slopes of Parallel Lines
m_1 = m_2
If two lines are parallel, their slopes are exactly the same. If you know the slopes of two lines are equal, you know the lines are parallel.
Rule for Slopes of Perpendicular Lines
m_1 * m_2 = -1
If two lines are perpendicular, the product of their slopes is -1. This means their slopes are 'negative reciprocals' (e.g., 3 and -1/3).
Vertical Angles Theorem
∠A = ∠C and ∠B = ∠D
When two lines intersect, they form two pairs of opposite angles called vertical angles. The angles in each pair are always equal to each other.
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Challenging
Line G has a slope of m = (x/3). Line H is perpendicular to Line G and has a slope of -1. What is the value of x?
A.-3
B.3
C.1/3
D.-1
Challenging
Line A has a slope of 2. Line B is parallel to Line A. Line C is perpendicular to Line B. Line D is parallel to Line C. What is the slope of Line D?
A.-1/2
B.2
C.1/2
D.-2
Challenging
On a coordinate plane, two distinct lines are both perpendicular to the line y = 5. What must be true about these two lines?
A.They are perpendicular to each other.
B.They are horizontal lines.
C.They intersect at the point (0,5).
D.They are parallel to each other.
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