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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Explore essential geometry terms with this flashcard quiz. Each card presents a key term along with its definition, helping you strengthen your understanding of geometric concepts. Perfect for students needing a quick review or anyone wanting to familiarize themselves with geometry terminology.

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