Grade 12 Geometric Logic Worksheet
Explore the principles of geometric logic with this Grade 12 worksheet, covering conditional statements, converses, inverses, contrapositives, and deductive reasoning in geometric contexts.
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Standards
Topics
Geometric Logic: Conditional Statements and Reasoning
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Read each question carefully and provide your answers in the spaces provided. Show all your work for full credit.
1. Which of the following is the contrapositive 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.
If a polygon is a square, then it does not have four equal sides.
2. Consider the statement: "If two lines are parallel, then they do not intersect." What is the inverse of this statement?
If two lines do not intersect, then they are parallel.
If two lines are not parallel, then they intersect.
If two lines intersect, then they are not parallel.
If two lines are parallel, then they intersect.
3. The of a conditional statement switches the hypothesis and the conclusion.
4. If a conditional statement is true, its is also always true.
5. Write a conditional statement, its converse, inverse, and contrapositive for the following geometric fact: "All equilateral triangles are isosceles triangles."
Conditional:
Converse:
Inverse:
Contrapositive:
6. The converse of a true statement is always true.
True
False
7. If two angles are supplementary, then their sum is 180 degrees. This is an example of deductive reasoning.
True
False
8. Given the following premises, use deductive reasoning to draw a valid conclusion:
Premise 1: If a quadrilateral is a rhombus, then it has four congruent sides.
Premise 2: Quadrilateral ABCD is a rhombus.
Conclusion: