Geometry Final Review Quiz & Flashcards

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Questions and Answers

Which are true regarding the statement 'a quadrilateral having exactly one pair of parallel opposite sides is a trapezoid'? (Select all that apply)

It is a conditional statement that can be written as 'if a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid' (correct)

The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides (correct)

It is a true statement

The conclusion is: it is a rectangle

What is the converse of the statement 'if a line is vertical then it has undefined slope'?

If a line has an undefined slope then it is a vertical line

What is the inverse of the statement 'if a line is vertical then it has undefined slope'?

If a line is not vertical then it does not have an undefined slope

What is the contrapositive of the statement 'if a line is horizontal then it has slope equal to zero'?

If a line does not have zero slope then it is not a horizontal line Signup and view all the answers

What is the contrapositive of the statement 'if there is a lightning storm then we won't go swimming'?

If we go swimming then there will not be a lightning storm Signup and view all the answers

What is a true conditional statement based on the diagram?

If a student is an honor student then he/she may also be a band member Signup and view all the answers

Match the conditional statement to its symbolic form:

~p → ~q = If today is not October 6, then it is not Nina's birthday q → p = If today is Nina's birthday then it is October 6 p → q = If today is October 6 then it is Nina's birthday ~q → ~p = If it is not Nina's birthday then today is not October 6 Signup and view all the answers

Determine the truth value of the statement: 'If 3 is an even number then 5 + 3 = 8'.

False Signup and view all the answers

What is equivalent to ~Q → ~P if P: N is a multiple of two and Q: N is an even number?

P → Q Signup and view all the answers

Identify the truth table for Q → P where Q represents a statement.

B; TTFF, TFTF, TTFT Signup and view all the answers

Which statement represents a true conclusion based on the Venn diagram?

Some numbers that are multiples of three are also even numbers Signup and view all the answers

The hypothesis of the statement 'if the last digit of N is zero then N is divisible by five' is: ______

The last digit of N is zero Signup and view all the answers

What is the conclusion of the statement: 'if the last digit of N is zero then N is divisible by five'?

N is divisible by five Signup and view all the answers

What is the converse of 'if Jack's pet is a pig then Jack's pet cannot fly'?

If Jack's pet cannot fly then Jack's pet is a pig Signup and view all the answers

What is the logically equivalent statement to Q → P where P is 'student achieves 90 percent on a geometry final' and Q is 'student will receive a passing grade in geometry class'?

If a student did not receive 90 percent on the geometry final then the student did not pass geometry class Signup and view all the answers

What is the contrapositive of 'if 3x + 7 = -5 then 4x + 12 = -4'?

If 4x + 12 ≠ -4, then 3x + 7 ≠ -5 Signup and view all the answers

What is the logically equivalent statement for the conditional statement P → ~Q?

Q → ~P Signup and view all the answers

Which pairs of statements are logically equivalent? (Select 2 options)

The converse and the inverse of the original conditional statement Signup and view all the answers

What is the inverse of P → Q?

If x - 5 ≠ 10, then 4x + 1 ≠ 61 Signup and view all the answers

What is the contrapositive of the original conditional statement represented by P → Q?

~Q → ~P Signup and view all the answers

What is the contrapositive of the statement: 'if two variables are directly proportional then their graph is a linear function'?

If the graph of two variables is not a linear function, then the two variables are not directly proportional Signup and view all the answers

What represents the inverse in the original conditional statement P → Q?

The inverse is represented by ~P → ~Q Signup and view all the answers

What is the alternative name for the inverse of a conditional statement?

The inverse of the original conditional statement Signup and view all the answers

What is the converse of 'if x is even then x + 1 is odd'?

If x + 1 is odd then x is even Signup and view all the answers

Study Notes

Quadrilaterals and Trapezoids

A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides.
Conditional statement format: "If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid."
In this conditional statement:
- Hypothesis: "A quadrilateral having exactly one pair of parallel opposite sides."
- Conclusion: "It is a trapezoid."

Converse and Inverse Statements

The converse of a statement flips the hypothesis and conclusion.
- For "If a line is vertical, then it has undefined slope," the converse is: "If a line has an undefined slope, then it is vertical."
The inverse negates both the hypothesis and conclusion.
- For the same statement, the inverse is: "If a line is not vertical, then it does not have an undefined slope."

Contrapositive

The contrapositive negates both parts and swaps them.
- For "If a line is horizontal, then it has a slope equal to zero," the contrapositive is: "If a line does not have zero slope, then it is not horizontal."

Conditional Statement Example

The conditional "If there is a lightning storm, then we won't go swimming" has the contrapositive: "If we go swimming, then there will not be a lightning storm."

True Conditional Statement

Based on a given diagram, a true statement could be: "If a student is an honor student, then he/she may also be a band member."

Symbolic Representation of Conditions

Statements can be represented symbolically:
- ~p → ~q: "If today is not October 6, then it is not Nina's birthday."
- q → p: "If today is Nina’s birthday, then it is October 6."
- p → q: "If today is October 6, then it is Nina's birthday."
- ~q → ~p: "If it is not Nina's birthday, then today is not October 6."

Truth Value of Conditional Statements

A false statement (e.g., "3 is an even number") implies a true statement, making the overall conditional false.

Equivalent Statements

The logic behind statements: ~Q → ~P is the inverse of P → Q, indicating that if N is not even, then it is not a multiple of two, which is equivalent to P → Q.

Converse and Inverse Evaluation

The inverse of "If you are human, then you were born on Earth" is true: "If you are not human, then you were not born on Earth."
The converse "If you were born on Earth, then you are human" is false because nonhuman creatures also exist on Earth.

Truth Tables

Based on the conditional expression Q → P, a truth table categorizes outcomes: TTFF, TFTF, TTFT.

Venn Diagram Conclusions

According to a Venn diagram, some numbers that are multiples of three are also even.

Statements and Their Relations

The relationship P: "Student achieves 90% on a geometry final" and Q: "Student will receive a passing grade in geometry class" shows that Q → P implies students not passing did not score 90%.

Logical Equivalence

In terms of logical equivalency, P → Q is equivalent to ~Q → ~P; both convey similar information about the statements' relationships.

Overall Connections

Understanding statements, converses, inverses, and contrapositives are critical in logical reasoning and geometry.
The equivalency of statements can often assist in deducing the truth of conditions based on given scenarios or hypotheses.

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Description

Test your understanding of trapezoids with this flashcard quiz. Focus on the conditional statements related to quadrilaterals and their properties. Check your knowledge on what defines a trapezoid and its characteristics.

Geometry Basics: Trapezoids Definition

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