Geometry Terms Flashcards

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.

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

What is the definition of a line?

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

What is a plane?

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

What is the definition of space in geometry?

The set of all points; 3D. Signup and view all the answers

What are collinear points?

Points on the same line. Signup and view all the answers

What are noncollinear points?

Points not on the same line. Signup and view all the answers

What are coplanar points?

Points in the same plane. Signup and view all the answers

What are noncoplanar points?

Points not in the same plane. Signup and view all the answers

Name the three undefined terms of geometry.

Point, line, plane. Signup and view all the answers

What is a postulate?

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

Define a segment.

Part of a line containing two endpoints. Signup and view all the answers

What is a ray?

One endpoint extending forever in one direction. Signup and view all the answers

What are opposite rays?

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

What are parallel lines?

Coplanar lines that NEVER intersect. Signup and view all the answers

Define perpendicular lines.

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

What are skew lines?

Noncoplanar lines; cannot be parallel. Signup and view all the answers

What does oblique mean?

Slanted. Signup and view all the answers

What are parallel planes?

Planes that don't touch. Signup and view all the answers

What are congruent segments?

Two or more segments with the same length. Signup and view all the answers

What is the segment addition postulate?

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

Define midpoint.

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

What is an angle?

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

What are congruent angles?

Angles with the same measure. Signup and view all the answers

Explain the angle addition postulate.

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

What is a perpendicular bisector?

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

What is an angle bisector?

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

What is a conditional statement?

'If, then' statements. Signup and view all the answers

What is a converse?

Statement that switches the hypothesis and the conclusion. Signup and view all the answers

What is an inverse?

Statement that negates the conditional (not). Signup and view all the answers

Define contrapositive.

Statement that is a combination of the converse and the inverse. Signup and view all the answers

What is a biconditional statement?

'Iff' (if and only if) statements. Signup and view all the answers

What is deductive reasoning?

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

What is the additional property?

If a = b, then a + c = b + c. Signup and view all the answers

What is the subtraction property?

If a = b, then a - c = b - c. Signup and view all the answers

Define multiplication property.

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

What is the division property?

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

Define the reflexive property.

a = a Signup and view all the answers

What is the symmetric property?

If a = b, then b = a. Signup and view all the answers

What is the transitive property?

If a = b and b = c, then a = c. Signup and view all the answers

What is the substitution property?

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

What is the distributive property?

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

What does combining like terms entail?

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

What are vertical angles?

Two angles sharing a vertex facing opposite directions. Signup and view all the answers

What are adjacent angles?

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

Define complementary angles.

Angles whose measures sum equals 90 degrees. Signup and view all the answers

What are supplementary angles?

Angles whose measures sum to 180 degrees. Signup and view all the answers

What is a theorem?

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

Define an acute angle.

An angle less than 90 degrees. Signup and view all the answers

What is a right angle?

An angle measuring 90 degrees. Signup and view all the answers

Define an obtuse angle.

An angle greater than 90 degrees. Signup and view all the answers

What is a straight angle?

An angle measuring 180 degrees. Signup and view all the answers

What does the term congruent mean?

The geometric word for 'equal'. Signup and view all the answers

What is a hypothesis in a conditional statement?

The part of the conditional statement following 'if'. Signup and view all the answers

What is a conclusion in a conditional statement?

The part of the conditional statement following 'then'. Signup and view all the answers

What is a transversal?

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

What are alternate interior angles?

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

What are alternate exterior angles?

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

What are same-side interior angles?

Interior angles on the same side of the transversal. Signup and view all the answers

What are same-side exterior angles?

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

Define corresponding angles.

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

What does transformation refer to in geometry?

Change in position, shape, and size. Signup and view all the answers

What is a preimage?

Original figure before a transformation. Signup and view all the answers

What is an image?

New figure after a transformation. Signup and view all the answers

Define isometry.

A transformation where the preimage and the image are congruent. Signup and view all the answers

What is a reflection in geometry?

A transformation where the figure is flipped. Signup and view all the answers

What is the line of reflection?

The way that a figure is flipped. Signup and view all the answers

What is a translation?

A transformation where the figure is slid. Signup and view all the answers

What is rotation?

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

What is the point of rotation?

The point from which a figure is rotated. Signup and view all the answers

Define symmetry.

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

What is reflectional symmetry?

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

What is rotational symmetry?

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

What is dilation?

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

What is enlargement in geometry?

The area of the figure increases with dilation. Signup and view all the answers

What does reduction mean?

The area of the figure decreases with dilation. Signup and view all the answers

What is a construction in geometry?

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

What are congruent polygons?

Figures that have congruent corresponding parts. Signup and view all the answers

What does the Triangle Angle-Sum Theorem state?

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

What are remote interior angles?

Two nonadjacent interior angles of a triangle. Signup and view all the answers

What does the Triangle Exterior Angle Theorem state?

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

Define the Third Angles Theorem.

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

What is the SSS Postulate?

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

What is the SAS Postulate?

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. Signup and view all the answers

What is the ASA Postulate?

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. Signup and view all the answers

What is the AAS Theorem?

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. Signup and view all the answers

What is the HL Theorem?

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. Signup and view all the answers

What is a proof in geometry?

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

What does CPCTC stand for?

Corresponding parts of congruent triangles are congruent. Signup and view all the answers

What is a midsegment in a triangle?

Segment of a triangle connecting the midpoints of two sides. Signup and view all the answers

What does the midsegment theorem state?

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

What are cevians?

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

What is a perpendicular bisector?

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

Define angle bisector.

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

What is a median in a triangle?

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

What is an altitude in a triangle?

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

Define concurrent lines.

When lines intersect at the same point. Signup and view all the answers

What is the point of concurrency?

The point where all of the lines converge. 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.