Geometric Logic Fundamentals
This worksheet covers fundamental concepts in geometric logic, including conditional statements, converses, inverses, contrapositives, and deductive reasoning.
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Geometric Logic Fundamentals
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Read each question carefully and provide your best answer. Show all your work for short answer questions.
1. Which of the following is the converse of the statement: "If a polygon is a square, then it has four sides"?
If a polygon has four sides, then it is a square.
If a polygon is not a square, then it does not have four sides.
If a polygon does not have four sides, then it is not a square.
A square has four sides.
2. What is the contrapositive of the statement: "If an angle is acute, then its measure is less than 90 degrees"?
If an angle's measure is less than 90 degrees, then it is acute.
If an angle is not acute, then its measure is not less than 90 degrees.
If an angle's measure is not less than 90 degrees, then it is not acute.
An acute angle measures less than 90 degrees.
3. A statement that can be written in the form "If p, then q" is called a statement.
4. The of a conditional statement switches the hypothesis and the conclusion.
5. The of a conditional statement negates both the hypothesis and the conclusion.
6. The inverse of a true conditional statement is always true.
True
False
7. If a conditional statement is true, its contrapositive is also true.
True
False
8. Consider the following statements:
Premise 1: If an animal is a dog, then it is a mammal.
Premise 2: Fido is a dog.
What conclusion can be drawn using the Law of Detachment?
9. Consider the following statements:
Premise 1: If it is raining, then the ground is wet.
Premise 2: If the ground is wet, then the car will get dirty.
What conclusion can be drawn using the Law of Syllogism?
10. Given the diagram below, complete the two-column proof.
Given: Line AB intersects line CD at point E. ∠AEC and ∠BED are vertical angles.
Prove: ∠AEC ≅ ∠BED
Statement
Reason
1. Line AB intersects line CD at point E.
1. Given
2. ∠AEC and ∠CEB form a linear pair.
2.
3. ∠CEB and ∠BED form a linear pair.
3.
4. ∠AEC and ∠CEB are supplementary.
4. Definition of Linear Pair
5. ∠CEB and ∠BED are supplementary.
5. Definition of Linear Pair
6. m∠AEC + m∠CEB = 180°
6. Definition of Supplementary Angles
7. m∠CEB + m∠BED = 180°
7. Definition of Supplementary Angles
8. m∠AEC + m∠CEB = m∠CEB + m∠BED
8.
9. m∠AEC = m∠BED
9. Subtraction Property of Equality
10. ∠AEC ≅ ∠BED
10.