All Geometry Theorems Flashcards
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All Geometry Theorems Flashcards

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Questions and Answers

What does 'congruent' mean?

  • A triangle with all sides equal
  • Two angles together add up to 180 degrees
  • Equal in size and shape (correct)
  • Lines that intersect at a 90 degree angle
  • What is a midpoint?

    The point in the middle of a segment that bisects the segment.

    What are parallel lines?

    Two lines that are on the same plane and do not intersect.

    What are perpendicular lines?

    <p>Lines that intersect at a 90 degree angle.</p> Signup and view all the answers

    What defines an isosceles triangle?

    <p>A triangle with two congruent sides.</p> Signup and view all the answers

    What are supplementary angles?

    <p>Angles that add up to 180 degrees.</p> Signup and view all the answers

    What are complementary angles?

    <p>Angles that add up to 90 degrees.</p> Signup and view all the answers

    What is a linear pair?

    <p>A pair of adjacent angles formed when two lines intersect.</p> Signup and view all the answers

    What is an angle bisector?

    <p>A ray that cuts an angle into two congruent angles.</p> Signup and view all the answers

    What is an altitude in a triangle?

    <p>A segment perpendicular from a vertex to the opposite side.</p> Signup and view all the answers

    What is a perpendicular bisector?

    <p>A line that is perpendicular to a side of a triangle and passes through the midpoint.</p> Signup and view all the answers

    What is a median in a triangle?

    <p>A segment from a vertex to the opposite side.</p> Signup and view all the answers

    What does the Ruler Postulate state?

    <p>Every point on a number line can be paired with a number and vice versa.</p> Signup and view all the answers

    What does the Segment Addition Postulate explain?

    <p>Adding two segments together creates a larger segment.</p> Signup and view all the answers

    What is the Protractor Postulate?

    <p>The extension of the Ruler Postulate with a protractor.</p> Signup and view all the answers

    What is the Angle Addition Postulate?

    <p>Two angles added together create one larger angle.</p> Signup and view all the answers

    What does the Addition Property state?

    <p>If a = b, then a + c = b + c.</p> Signup and view all the answers

    What does the Subtraction Property indicate?

    <p>If a = b, then a - c = b - c.</p> Signup and view all the answers

    What is the Multiplication Property?

    <p>If a = b, then a times c = b times c.</p> Signup and view all the answers

    What does the Division Property state?

    <p>If a = b, then a divided by c = b divided by c.</p> Signup and view all the answers

    What is the Substitution Property?

    <p>If a = b, then a can replace b in any expression.</p> Signup and view all the answers

    What does the Reflexive Property express?

    <p>A = A.</p> Signup and view all the answers

    What is the Symmetric Property?

    <p>If a = b, then b = a.</p> Signup and view all the answers

    What does the Transitive Property state?

    <p>If a = b and b = c, then a = c.</p> Signup and view all the answers

    What is the Distributive Property?

    <p>If a(b + c), then ab + ac.</p> Signup and view all the answers

    What is Postulate 5?

    <p>A line contains at least 2 points, a plane contains at least 3 points, and space contains at least 4 points.</p> Signup and view all the answers

    What is Postulate 6?

    <p>Through any two points, there is exactly one line.</p> Signup and view all the answers

    What is Postulate 7?

    <p>Through any three points, there is at least one plane.</p> Signup and view all the answers

    What is Postulate 8?

    <p>If two planes intersect, then their intersection is a line.</p> Signup and view all the answers

    What is Postulate 9?

    <p>If two planes intersect, then their intersection is a line.</p> Signup and view all the answers

    What does the SSS Postulate state?

    <p>If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.</p> Signup and view all the answers

    What does the SAS Postulate indicate?

    <p>If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.</p> Signup and view all the answers

    What does the ASA Postulate state?

    <p>If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.</p> Signup and view all the answers

    What does Theorem 1-1 state?

    <p>If two lines intersect, then they intersect in exactly one point.</p> Signup and view all the answers

    What does Theorem 1-2 indicate?

    <p>Through a line and a point not on the line, there is exactly one plane.</p> Signup and view all the answers

    What does Theorem 1-3 state?

    <p>If two lines intersect, then exactly one plane contains the lines.</p> Signup and view all the answers

    Study Notes

    Key Geometry Terms and Definitions

    • Congruent: Figures or shapes that are identical in size and shape.
    • Midpoint: The specific point that divides a segment into two equal parts, resulting in two congruent segments.
    • Parallel Lines: Lines that remain equidistant and never intersect, existing on the same plane.
    • Perpendicular Lines: Lines that cross each other at an exact right angle (90 degrees).

    Triangle Properties

    • Isosceles Triangle: A triangle that has at least two sides of equal length, creating two congruent angles.
    • Altitude: A line segment from a vertex to the opposite side, forming a right angle with that side; represents the triangle's height.
    • Median: A line segment that connects a vertex of the triangle to the midpoint of the opposite side.

    Angle Relationships

    • Supplementary Angles: Two angles whose measures add up to 180 degrees.
    • Complementary Angles: Two angles that combine to equal 90 degrees.
    • Linear Pair: A pair of adjacent angles formed when two lines intersect, yielding a straight line.

    Angle Bisector

    • Angle Bisector: A ray that divides an angle into two equal parts, creating two congruent angles.

    Line Properties

    • Perpendicular Bisector: A line that divides a side of a triangle into two equal segments at a right angle.
    • Protractor Postulate: Every angle can be measured in degrees using a protractor, similar to how points are measured on a number line.

    Postulates and Properties

    • Ruler Postulate: Establishes that each point on a line corresponds uniquely to a number.
    • Segment Addition Postulate: The sum of two segments along a line equals the larger segment formed.
    • Angle Addition Postulate: The sum of two angles equal a larger angle.

    Algebraic Properties

    • Addition Property: If two quantities are equal, adding the same value to both maintains equality.
    • Subtraction Property: Similar to addition, subtracting the same value from both sides keeps equality intact.
    • Multiplication Property: Multiplying both sides of an equation by the same value preserves equality.
    • Division Property: Dividing both sides by the same non-zero number keeps the equation balanced.
    • Substitution Property: An expression can be replaced with an equal expression in any equation.

    Logical Properties

    • Reflexive Property: Any quantity is equal to itself.
    • Symmetric Property: If one quantity equals another, the converse is also true.
    • Transitive Property: If one quantity equals a second, and that second equals a third, then the first equals the third.

    Geometric Postulates about Points and Lines

    • Postulate 5: At least two points are required to form a line; at least three non-collinear points form a plane.
    • Postulate 6: Exactly one line can be drawn through any two points.
    • Postulate 7: At least one plane exists through any three points, with exactly one plane possible for three non-collinear points.
    • Postulate 8 & 9: The intersection of two planes results in a line.

    Triangle Congruence Postulates

    • SSS Postulate: Triangles are congruent if all three sides of one triangle are equal to those of another.
    • SAS Postulate: If two sides and the included angle of one triangle are congruent to the corresponding parts of another, the triangles are congruent.
    • ASA Postulate: Two angles and the included side are sufficient to prove triangle congruence.

    Intersection Theorems

    • Theorem 1-1: Two intersecting lines will intersect at a single point.
    • Theorem 1-2: There is one unique plane that contains a line and a point not on that line.
    • Theorem 1-3: Two intersecting lines lie in exactly one plane.

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    Test your knowledge of geometry theorems with these flashcards. Each card features a key term along with its definition, helping you understand important concepts such as congruence, midpoints, and line relationships. Perfect for students and geometry enthusiasts alike!

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