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Geometry Unit 3: Parallel & Perpendicular Lines
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Geometry Unit 3: Parallel & Perpendicular Lines

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@BeneficentHonor6192

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?

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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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