Geometric Logic Fundamentals
This worksheet covers fundamental concepts in geometric logic, including conditional statements, converses, inverses, contrapositives, and deductive reasoning applied to geometric figures.
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Geometric Logic Fundamentals
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Read each question carefully and provide your best answer. Show all work for problems requiring calculations or explanations.
1. Which of the following is the converse of the statement: "If a polygon is a square, then it has four equal sides"?
If a polygon has four equal sides, then it is a square.
If a polygon is not a square, then it does not have four equal sides.
If a polygon does not have four equal sides, then it is not a square.
A square has four equal sides.
2. The contrapositive of a true conditional statement is always:
True
False
Sometimes true, sometimes false
Logically equivalent to the inverse
3. The statement "If two angles are vertical angles, then they are congruent" is a statement.
4. The of "If two lines are parallel, then they never intersect" is "If two lines intersect, then they are not parallel."
5. Given the conditional statement: "If a triangle has three equal sides, then it is an equilateral triangle."
a. Write the inverse of the statement.
b. Write the contrapositive of the statement.
6. The converse of a true statement is always true.
True
False
7. If a conditional statement is false, then its contrapositive is also false.
True
False
8. Consider the following statements:
Premise 1: All squares are rectangles.
Premise 2: Figure ABCD is a square.
What conclusion can be drawn from these premises using deductive reasoning?
9. Look at the diagram below.
If Side 1 is congruent to Side 2, what type of triangle is it? Justify your answer using a conditional statement.
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