Law of Detachment Worksheet
Grade 10 Math worksheet covering the Law of Detachment with various question types.
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Law of Detachment Worksheet
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Read each statement carefully and apply the Law of Detachment to determine the valid conclusion. If no valid conclusion can be drawn, write 'No valid conclusion'.
1. If a polygon is a square, then it has four equal sides. Polygon ABCD is a square. Therefore, .
2. If a student studies diligently, then they will pass the exam. Sarah passed the exam. Therefore, .
3. If it rains, the ground gets wet. It is raining. Therefore, .
4. If a number is divisible by 10, then it is divisible by 5. The number 70 is divisible by 10. Therefore, .
5. Given: If an animal is a dog, then it barks. Fido barks. Conclusion: Fido is a dog.
True
False
6. Given: If a quadrilateral is a rectangle, then it has four right angles. Figure XYZW is a rectangle. Conclusion: Figure XYZW has four right angles.
True
False
7. State the Law of Detachment in your own words.
8. Write a conditional statement and a true hypothesis that allows you to use the Law of Detachment to draw a conclusion.
9. Which of the following is a valid conclusion based on the Law of Detachment?
Premise 1: If an angle is acute, then its measure is less than 90 degrees.
Premise 2: Angle A has a measure of 45 degrees.
Angle A is acute.
Angle A is not obtuse.
The measure of Angle A is not 90 degrees.
No valid conclusion can be drawn.
10. Consider the following statements: If a quadrilateral is a rhombus, then it has four congruent sides. Quadrilateral PQRS has four congruent sides. What conclusion can be drawn?
Quadrilateral PQRS is a rhombus.
Quadrilateral PQRS is a square.
Quadrilateral PQRS has four right angles.
No valid conclusion can be drawn.
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