Conditional Statements Worksheet
A Grade 10 Math worksheet covering conditional statements, converses, inverses, and contrapositives with real-world examples and logical reasoning exercises.
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Conditional Statements
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Read each question carefully and follow the instructions. Show all your work where applicable.
Identify the hypothesis and conclusion in the following conditional statements.
1. If a polygon has three sides, then it is a triangle.
Hypothesis:
Conclusion:
2. If a number is even, then it is divisible by 2.
Hypothesis:
Conclusion:
3. What is the converse of the statement: "If it is raining, then the ground is wet"?
If the ground is wet, then it is raining.
If it is not raining, then the ground is not wet.
If the ground is not wet, then it is not raining.
It is raining and the ground is wet.
4. What is the inverse of the statement: "If a figure is a square, then it has four equal sides"?
If a figure has four equal sides, then it is a square.
If a figure is not a square, then it does not have four equal sides.
If a figure does not have four equal sides, then it is not a square.
A figure is a square if and only if it has four equal sides.
Determine whether the following statements are true or false.
5. The inverse of a true conditional statement is always true.
True
False
6. A conditional statement and its contrapositive always have the same truth value.
True
False
7. Rewrite the following statement as a conditional statement (If-Then form): "All birds have feathers."
8. Write the contrapositive of the statement: "If a quadrilateral is a rectangle, then it has four right angles."
Match each term with its definition.
9. Conditional Statement
a. Formed by negating both the hypothesis and conclusion of the converse.
10. Converse
b. An 'If-Then' statement.
11. Inverse
c. Formed by switching the hypothesis and conclusion.
12. Contrapositive
d. Formed by negating both the hypothesis and conclusion.
13. When can a conditional statement be written as a biconditional statement?
14. Write the following statement as a biconditional statement: "If two angles are congruent, then they have the same measure."