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Geometry Terms Flashcards
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Geometry Terms Flashcards

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Questions and Answers

What is the definition of inductive reasoning?

  • A statement/conclusion drawn from reasoning
  • Proves the conjecture to be false
  • Based on observation; pattern (correct)
  • No shape, no size; represents a location in space
  • What is a conjecture?

    A statement/conclusion drawn from reasoning.

    What does a counterexample do?

    Proves the conjecture to be false.

    Define a point.

    <p>No shape, no size; represents a location in space.</p> Signup and view all the answers

    What is the definition of a line?

    <p>The set of points extending in two opposite directions forever.</p> Signup and view all the answers

    What is a plane?

    <p>A 2D flat surface extending in all directions forever.</p> Signup and view all the answers

    What is the definition of space in geometry?

    <p>The set of all points; 3D.</p> Signup and view all the answers

    What are collinear points?

    <p>Points on the same line.</p> Signup and view all the answers

    What are noncollinear points?

    <p>Points not on the same line.</p> Signup and view all the answers

    What are coplanar points?

    <p>Points in the same plane.</p> Signup and view all the answers

    What are noncoplanar points?

    <p>Points not in the same plane.</p> Signup and view all the answers

    Name the three undefined terms of geometry.

    <p>Point, line, plane.</p> Signup and view all the answers

    What is a postulate?

    <p>Accepted as fact (doesn't have to be proven); also known as an axiom.</p> Signup and view all the answers

    Define a segment.

    <p>Part of a line containing two endpoints.</p> Signup and view all the answers

    What is a ray?

    <p>One endpoint extending forever in one direction.</p> Signup and view all the answers

    What are opposite rays?

    <p>Two rays going in opposite directions, forming a line and sharing an endpoint.</p> Signup and view all the answers

    What are parallel lines?

    <p>Coplanar lines that NEVER intersect.</p> Signup and view all the answers

    Define perpendicular lines.

    <p>Coplanar lines that intersect to form four right angles.</p> Signup and view all the answers

    What are skew lines?

    <p>Noncoplanar lines; cannot be parallel.</p> Signup and view all the answers

    What does oblique mean?

    <p>Slanted.</p> Signup and view all the answers

    What are parallel planes?

    <p>Planes that don't touch.</p> Signup and view all the answers

    What are congruent segments?

    <p>Two or more segments with the same length.</p> Signup and view all the answers

    What is the segment addition postulate?

    <p>If we know AB and BC, then we can find AC.</p> Signup and view all the answers

    Define midpoint.

    <p>A point that divides a segment into two congruent segments.</p> Signup and view all the answers

    What is an angle?

    <p>Formed by two rays (sides) with the same endpoint (vertex).</p> Signup and view all the answers

    What are congruent angles?

    <p>Angles with the same measure.</p> Signup and view all the answers

    Explain the angle addition postulate.

    <p>The measures of smaller angles add up to the measure of the larger angle.</p> Signup and view all the answers

    What is a perpendicular bisector?

    <p>A line, segment, or ray that is perpendicular to a segment at its midpoint.</p> Signup and view all the answers

    What is an angle bisector?

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

    What is a conditional statement?

    <p>'If, then' statements.</p> Signup and view all the answers

    What is a converse?

    <p>Statement that switches the hypothesis and the conclusion.</p> Signup and view all the answers

    What is an inverse?

    <p>Statement that negates the conditional (not).</p> Signup and view all the answers

    Define contrapositive.

    <p>Statement that is a combination of the converse and the inverse.</p> Signup and view all the answers

    What is a biconditional statement?

    <p>'Iff' (if and only if) statements.</p> Signup and view all the answers

    What is deductive reasoning?

    <p>Intuition (coming from previous/prior knowledge).</p> Signup and view all the answers

    What is the additional property?

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

    What is the subtraction property?

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

    Define multiplication property.

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

    What is the division property?

    <p>If a = b and c ≠ 0, then a/c = b/c.</p> Signup and view all the answers

    Define the reflexive property.

    <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 is the transitive property?

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

    What is the substitution property?

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

    What is the distributive property?

    <p>4(5x + 2) = 20x + 8.</p> Signup and view all the answers

    What does combining like terms entail?

    <p>12x + 7y + 6x + 2x + 8y - 3x - 2y = 17x + 13y (CLT).</p> Signup and view all the answers

    What are vertical angles?

    <p>Two angles sharing a vertex facing opposite directions.</p> Signup and view all the answers

    What are adjacent angles?

    <p>Angles that are side by side (shares a vertex and common side).</p> Signup and view all the answers

    Define complementary angles.

    <p>Angles whose measures sum equals 90 degrees.</p> Signup and view all the answers

    What are supplementary angles?

    <p>Angles whose measures sum to 180 degrees.</p> Signup and view all the answers

    What is a theorem?

    <p>A proven mathematical concept that was once a theory.</p> Signup and view all the answers

    Define an acute angle.

    <p>An angle less than 90 degrees.</p> Signup and view all the answers

    What is a right angle?

    <p>An angle measuring 90 degrees.</p> Signup and view all the answers

    Define an obtuse angle.

    <p>An angle greater than 90 degrees.</p> Signup and view all the answers

    What is a straight angle?

    <p>An angle measuring 180 degrees.</p> Signup and view all the answers

    What does the term congruent mean?

    <p>The geometric word for 'equal'.</p> Signup and view all the answers

    What is a hypothesis in a conditional statement?

    <p>The part of the conditional statement following 'if'.</p> Signup and view all the answers

    What is a conclusion in a conditional statement?

    <p>The part of the conditional statement following 'then'.</p> Signup and view all the answers

    What is a transversal?

    <p>A line that intersects two coplanar lines at two distinct points.</p> Signup and view all the answers

    What are alternate interior angles?

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

    What are alternate exterior angles?

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

    What are same-side interior angles?

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

    What are same-side exterior angles?

    <p>Exterior angles that lie on the same side of the transversal.</p> Signup and view all the answers

    Define corresponding angles.

    <p>Angles on the same side of the transversal and in corresponding positions relative to the two lines.</p> Signup and view all the answers

    What does transformation refer to in geometry?

    <p>Change in position, shape, and size.</p> Signup and view all the answers

    What is a preimage?

    <p>Original figure before a transformation.</p> Signup and view all the answers

    What is an image?

    <p>New figure after a transformation.</p> Signup and view all the answers

    Define isometry.

    <p>A transformation where the preimage and the image are congruent.</p> Signup and view all the answers

    What is a reflection in geometry?

    <p>A transformation where the figure is flipped.</p> Signup and view all the answers

    What is the line of reflection?

    <p>The way that a figure is flipped.</p> Signup and view all the answers

    What is a translation?

    <p>A transformation where the figure is slid.</p> Signup and view all the answers

    What is rotation?

    <p>A transformation where the figure is turned (clockwise or counterclockwise).</p> Signup and view all the answers

    What is the point of rotation?

    <p>The point from which a figure is rotated.</p> Signup and view all the answers

    Define symmetry.

    <p>When the figure is divided, it is equal on both sides.</p> Signup and view all the answers

    What is reflectional symmetry?

    <p>When you can draw a line, flip the figure, and it is still the same.</p> Signup and view all the answers

    What is rotational symmetry?

    <p>A circular idea where you can rotate the figure and end up with the same shape eventually.</p> Signup and view all the answers

    What is dilation?

    <p>A transformation in which the size of the figure is enlarged or reduced.</p> Signup and view all the answers

    What is enlargement in geometry?

    <p>The area of the figure increases with dilation.</p> Signup and view all the answers

    What does reduction mean?

    <p>The area of the figure decreases with dilation.</p> Signup and view all the answers

    What is a construction in geometry?

    <p>A performed action using a ruler and compass, that is used to construct the mathematical structure of a figure.</p> Signup and view all the answers

    What are congruent polygons?

    <p>Figures that have congruent corresponding parts.</p> Signup and view all the answers

    What does the Triangle Angle-Sum Theorem state?

    <p>The sum of the measures of the interior angles of a triangle is 180 degrees.</p> Signup and view all the answers

    What are remote interior angles?

    <p>Two nonadjacent interior angles of a triangle.</p> Signup and view all the answers

    What does the Triangle Exterior Angle Theorem state?

    <p>The measure of an exterior angle is equal to the sum of its remote interior angles.</p> Signup and view all the answers

    Define the Third Angles Theorem.

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

    What is the SSS Postulate?

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

    What is the SAS Postulate?

    <p>If two sides and the included angle of a 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 is the ASA Postulate?

    <p>If two angles and the included side of a 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 is the AAS Theorem?

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

    What is the HL Theorem?

    <p>If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.</p> Signup and view all the answers

    What is a proof in geometry?

    <p>A method of proving a concept by several steps.</p> Signup and view all the answers

    What does CPCTC stand for?

    <p>Corresponding parts of congruent triangles are congruent.</p> Signup and view all the answers

    What is a midsegment in a triangle?

    <p>Segment of a triangle connecting the midpoints of two sides.</p> Signup and view all the answers

    What does the midsegment theorem state?

    <p>A midsegment is parallel to the non-connected side and half its length.</p> Signup and view all the answers

    What are cevians?

    <p>Special segments whose concepts were developed by Italian mathematician Giovanni Ceva.</p> Signup and view all the answers

    What is a perpendicular bisector?

    <p>A line, segment, or ray that is perpendicular to a segment and intersects it at its midpoint.</p> Signup and view all the answers

    Define angle bisector.

    <p>A segment or ray that divides an angle into two equal parts.</p> Signup and view all the answers

    What is a median in a triangle?

    <p>Segment going from a vertex to the midpoint of the opposite side.</p> Signup and view all the answers

    What is an altitude in a triangle?

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

    Define concurrent lines.

    <p>When lines intersect at the same point.</p> Signup and view all the answers

    What is the point of concurrency?

    <p>The point where all of the lines converge.</p> Signup and view all the answers

    Study Notes

    Inductive Reasoning and Conjectures

    • Inductive reasoning relies on observations to identify patterns.
    • A conjecture is a conclusion drawn from reasoning or observations and can be proven or disproven.

    Geometric Fundamentals

    • A point has no shape or size and represents a specific location in space.
    • A line is a set of points extending infinitely in two directions.
    • A plane is a two-dimensional flat surface extending infinitely.
    • Space encompasses all points in three dimensions.

    Collinearity and Coplanarity

    • Collinear points lie on the same line, while noncollinear points do not.
    • Coplanar points exist within the same plane; noncoplanar points do not.

    Undefined Terms and Postulates

    • The three undefined terms in geometry are point, line, and plane.
    • A postulate is an accepted fact that does not require proof, also termed as an axiom.

    Line Segments and Rays

    • A segment consists of part of a line with two endpoints.
    • A ray has one endpoint and extends infinitely in one direction.
    • Opposite rays are two rays extending in opposite directions from a common endpoint.

    Parallel and Perpendicular Lines

    • Parallel lines are coplanar and never intersect.
    • Perpendicular lines intersect to form four right angles.
    • Skew lines are noncoplanar and cannot be parallel.

    Angle Fundamentals

    • An angle is formed by two rays sharing a common endpoint called the vertex.
    • Congruent angles have the same measure, while vertical angles are pairs of opposite angles formed by intersecting lines.

    Angle Relationships

    • Complementary angles sum to 90 degrees.
    • Supplementary angles sum to 180 degrees.
    • The angle addition postulate allows for the determination of an angle's measure through the sum of smaller angles.

    Triangle and Angle Theorems

    • The Triangle Angle-Sum Theorem states that the sum of angles in a triangle is always 180 degrees.
    • Remote interior angles are nonadjacent interior angles that relate to an exterior angle according to the Triangle Exterior Angle Theorem.

    Congruence Postulates

    • SSS, SAS, ASA, AAS, and HL are congruence postulates and theorems dictating when triangles are congruent based on their sides and angles.

    Properties of Equality

    • The reflexive, symmetric, transitive, and substitution properties describe how equalities function in mathematical expressions.
    • The distributive property allows for the multiplication to be distributed over addition.

    Transformations and Symmetry

    • Transformations change a figure's position, shape, or size, including translations (sliding), rotations (turning), and reflections (flipping).
    • Symmetry exists when a figure can be divided equally, either through reflectional or rotational symmetry.

    Congruent Figures and Polygons

    • Congruent polygons have congruent corresponding parts, including sides and angles.
    • Midsegments of triangles connect midpoints of two sides and are parallel to the non-connected side.

    Proofs and Logical Reasoning

    • Proofs are structured methods for validating mathematical concepts through logical steps.
    • CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used after proving triangle congruence.

    Special Segments in Triangles

    • Medians connect vertices to midpoints, altitudes drop perpendicular from a vertex to the opposite side, and angle bisectors divide angles into two equal parts.
    • Concurrent lines meet at a single point called the point of concurrency.
    • Alternate interior angles lie on opposite sides of a transversal and are nonadjacent.
    • Corresponding angles are in the same position relative to the traversing line and the two intersected lines.

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