Name: _________________________________________________________
Date: ____________________________
Geometry
Ch. 2: Reasoning & Proof
Review Sheet: 2.1- 2.5
Part I: Continue the patterns.
1. Sketch the fourth figure in the pattern below.
2. Write the next three numbers in the pattern.
0, 1, 3, 6, _______________, _______________, _______________
Part II: Show the conjecture is false by finding a counterexample.
3. All intersecting planes form right angles.
Counterexample: _______________________________
4. The value of x3 is always greater then the value of x. Counterexample: _______________________________
5. Regular polygons always have an even number of sides.
Counterexample: _______________________
Part III: Write the If-then form, the converse, the inverse, and the contrapositive of the statement “A
poet is a writer.”
6. If-then form: __________________________________________________________________________________________________
7. Converse: _____________________________________________________________________________________________________
8. Inverse: _______________________________________________________________________________________________________
9. Contrapositive: _______________________________________________________________________________________________
Part IV: Rewrite the definition as a biconditional.
10. In an equilateral polygon, all sides are congruent.
Biconditional: ___________________________________________________________________________________________________
Part V: Use the Law of Detachment or the Law of Syllogism to make a valid conclusion in the
situation.
11. If you save $2000, then you can buy a car. You have saved $1200.
Conclusion: _____________________________________________________________________________________
12. The bakery makes a profit if its revenue is greater than its costs. You will get a raise if the baker
makes a profit.
Conclusion: ___________________________________________________________________________________________
Part VI: Provide a counterexample to prove the statement is false.
13. If the product of two numbers is positive, then the two numbers must both be positive.
Counterexample: _________________________________
14. All prime numbers are odd.
Counterexample: _______________
15. If the product of two numbers is even, then the two numbers must both be even.
Counterexample: _______________________________
Part V: Solve the equation. Justify each step.
16. 3x – 12 = 7x + 8
Given
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17. 5(x – 1) = 4x + 13
Given
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