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# Geometry Unit 3: Parallel & Perpendicular Lines

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@BeneficentHonor6192

### What is the definition of slope?

• Two angles whose sum is 90 degrees
• Two lines in the same plane that do not intersect
• A pair of opposite congruent angles formed by intersecting lines
• The steepness of a line on a graph, rise over run (correct)

False

### What does it mean for two lines to be perpendicular?

Two lines that intersect to form right angles.

### The inverse of a fraction is called a ______.

<p>reciprocal</p> Signup and view all the answers

### What are opposite reciprocals?

<p>Two numbers whose product is negative 1</p> Signup and view all the answers

### What are complementary angles?

<p>Two angles whose sum is 90 degrees.</p> Signup and view all the answers

### What are supplementary angles?

<p>Two angles whose sum is 180 degrees.</p> Signup and view all the answers

### What is a linear pair?

<p>A pair of adjacent angles whose non-common sides are opposite rays.</p> Signup and view all the answers

### What are vertical angles?

<p>A pair of opposite congruent angles formed by intersecting lines.</p> Signup and view all the answers

### Congruent angles have different measures.

<p>False</p> Signup and view all the answers

### What is a transversal line?

<p>A line that intersects two or more lines.</p> Signup and view all the answers

### What is the slope-intercept form of a line?

<p>y=mx+b, where m is the slope and b is the y-intercept.</p> Signup and view all the answers

### What is point-slope form?

<p>y-y₁=m(x-x₁), where m is the slope and (x₁,y₁) is a given point on the line.</p> Signup and view all the answers

### What are alternate interior angles?

<p>Two interior angles that lie on opposite sides of the transversal.</p> Signup and view all the answers

### What are alternate exterior angles?

<p>Two exterior angles that lie on opposite sides of the transversal.</p> Signup and view all the answers

### What are same side interior angles?

<p>Two interior angles on the same side of the transversal.</p> Signup and view all the answers

### What are same side exterior angles?

<p>Two exterior angles on the same side of the transversal.</p> Signup and view all the answers

### What are corresponding angles?

<p>Angles in the same place in the intersection on different lines.</p> Signup and view all the answers

### I cannot use _________ when proving lines are parallel.

<p>Vertical Angles &amp; Linear Pairs</p> Signup and view all the answers

### What is the symbol for parallel lines?

<p>||</p> Signup and view all the answers

### What is the symbol for perpendicular lines?

<p>upside down T</p> Signup and view all the answers

### What is the definition of a perpendicular line through a point on the line construction?

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### What is the definition of a perpendicular line through a point NOT on the line construction?

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### What is the definition of parallel lines construction?

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## Study Notes

### Slope and Lines

• Slope measures the steepness of a line on a graph, calculated as rise over run (m = (y-y)/(x-x)).
• Parallel lines have the same slope and never intersect.
• Perpendicular lines intersect at right angles with opposite reciprocal slopes.

### Angle Relationships

• Complementary angles sum to 90 degrees.
• Supplementary angles sum to 180 degrees.
• Linear pairs consist of adjacent angles with non-common sides as opposite rays, always supplementary.
• Vertical angles are formed by intersecting lines and are opposite congruent angles.

### Transformations and Forms

• The reciprocal of a fraction is obtained by flipping it.
• Opposite reciprocals are two numbers whose product equals -1 (e.g., 3/2 and -2/3).
• Slope-intercept form of a line is represented as y = mx + b, where m is the slope and b is the y-intercept.
• Point slope form is given by y - y₁ = m(x - x₁), where m is the slope, and (x₁, y₁) is a specific point on the line.

### Angle Relationships with Transversals

• Alternate interior angles are congruent and located on opposite sides of the transversal.
• Alternate exterior angles are also congruent and found outside the parallel lines on opposite sides of the transversal.
• Same side interior angles are supplementary and found on the same side of the transversal.
• Same side exterior angles are supplementary as well and located outside on the same side of the transversal.
• Corresponding angles are congruent and are found in the same position relative to the intersection of the transversal and the parallel lines.

### Symbols and Constructions

• The parallel symbol is represented as ||.
• The perpendicular symbol resembles an upside-down "T".
• Certain angle properties cannot be used to prove lines are parallel, specifically vertical angles and linear pairs.

### Construction Techniques

• Methods for constructing perpendicular lines through a point on or not on a given line are fundamental in geometry.
• Techniques for constructing parallel lines are essential for maintaining equidistance between lines.

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## Description

Test your knowledge on essential concepts related to parallel and perpendicular lines with these flashcards. Learn the definitions, slopes, and characteristics that define these geometric relationships.

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