Geometry Unit 3: Parallel & Perpendicular Lines
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Questions and Answers

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)

    • Parallel lines intersect each other.

    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?

    Signup and view all the answers

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

    Signup and view all the answers

    What is the definition of parallel lines construction?

    Signup and view all the answers

    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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    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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