Geometry Unit 1 Apex Review

What best describes the meaning of the term theorem?

A conclusion proved by deductive reasoning.

Venn Diagram

A diagram that uses two or more circles or other shapes to represent sets. Elements that belong to more than one set are placed in the areas where the circles overlap.

Syllogism

A form of deductive reasoning that combines two or more related conditional statements in order to arrive at a conclusion.

Line of symmetry

A line that divides a figure into two congruent halves that are mirror images of each other.

Proof

A logical arrangement of definitions, theorems, and postulates that leads to the conclusion that a statement is always true.

What divides a line segment into two congruent segments?

A midpoint

What is two-dimensional and infinitely large?

A plane

What is a zero-dimensional geometric object?

A point

Converse Statement

A statement in the form "If B, then A," given the statement "If A, then B." It is a flipped version of the original statement and is usually false.

Inverse Statement

A statement in the form "If not A, then not B," given the statement "If A, then B." It is a negated version of the original statement and is usually false.

Contrapositive Statement

A statement in the form "If not B, then not A," given the statement "If A, then B." It is a flipped, then negated version of the original statement and is usually true.

Conjecture

A statement that appears to be correct based on observation but has not been proven or disproven.

Definition

A statement that describes the qualities of an idea, object, or process.

Theorem

A statement that has already been proven to be true.

Conditional statement

A statement that has the form "If A, then B," where A is what you assume is true and B is the conclusion.

Postulate

A statement that is assumed to be true without proof. Also called an axiom.

Common Notion

A statement that is not officially defined but that is understood to be common sense.

Corollary

A statement that makes sense based on a statement that has already been proven (that is, a theorem).

Two Column Proof

A type of proof that has two columns: a left-hand column for statements, or deductions, and a right-hand column for the reason for each statement (that is, a definition, postulate, or theorem).

Indirect Proof

A type of proof that is written in paragraph form, where the contradiction of the statement to be proved is shown to be false, so the statement to be proved is therefore true. Also called proof by contradiction

Deduction

A way of thinking that starts with a given set of rules and conditions and figures out what must be true based on what is given.

Induction

A way of thinking that uses observations to form a general rule.

If point C is between points A and B, then AC + CB =

AB

Four points are always coplanar if:

All of them are collinear and they lie in same plane

Vertical angles must:

Be congruent and have the same vertex

Two or more points are _________ if they lie on the same line

Collinear

Which of the following are accepted without proof in a logical system?

Common notions, axioms, and postulates

Which type of statement has the form, "If A, then B."?

Conditional statement

Which types of statements can explain the steps of a proof?

Corollaries, definitions, and postulates

True or False: A theorem is a statement that can easily be proved using a corollary.

False

True or False: If you took a true "if-then" statement and inserted a not in each clause, the new statement would also be true.

False

True or False: Induction is a kind of thinking you use to get specific answers from a general rule.

False

True or false: A theorem is easily disproved.

False

When is a statement true? When is it false?

For a statement to be true, it must be true for every possible case. A statement is only true if there are no exceptions. For a statement to be false, it must be false in at least one possible case.

What is three-dimensional and infinitely large?

Geometric space

A flowchart proof uses a(n) form to present a logical argument.

Graphical

Which best describes the meaning of the statement, "If A then B."?

If A is true, then B must be true.

The set of all points in a plane that are equidistant from two points is a(n):

Line

A part of a line with endpoints on both ends is a(n):

Line segment

Which of the following are one-dimensional and have infinite length?

Lines and rays

What term describes lines that meet at right angles?

Perpindicular

Which of the following can be used to explain a statement in a geometric proof?

Postulate, theorem, corollary, and definition.

What term best describes a proof in which you assume the opposite of what you want to prove?

Proof by contradiction

In geometry, you can use deductive rules to:

Prove conjectures

Name some zero-dimensional or one-dimensional figures

Segment, ray, line, and a point

Lines that aren't in the same plane are called:

Skew lines

Symmetry

The property of having a line, or axis, that divides a given shape into two identical parts. A shape can have more than one line of symmetry.

Which of the following are always true in a logical system?

Theorems, corollaries, and postulates

Two lines and a point are guaranteed to be coplanar if:

They lie in the same plane

If three points are collinear, then they are coplanar.

True

True or False: If you took a true "if-then" statement, inserted not in each clause, and reversed the clauses, the new statement would also be true.

True

True or False: In a two-column proof, the left column contains a series of deductions.

True

True or False: In a two-column proof, the right column states your reasons.

True

True or False: In deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence.

True

True or False: In the body of an indirect proof, you must show that the assumption leads to the contradiction.

True

True or False: Postulates are accepted to be true without proof.

True

True or False: You can rely solely upon deduction to prove that your conclusion is correct.

True

True or false: To begin an indirect proof, you assume that the contradiction of what you want to prove is true.

True

What can you determine when you use deduction and start from a given set of rules and conditions?

What must be true

What is one way to use induction?

to divide what you see into groups of objects that share a characteristic or property