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Honors Geometry
2.1/2.3 Inductive and Deductive Reasoning Practice
Name: ____________________________________
Describe a pattern in the numbers. Write the next number in the pattern.
1.
1 3 5 7
, , ,
3 4 5 6
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2. 2, 5, 11, 23
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Make a conjecture about each value or geometric relationship.
3. The relationship between AP and PB, if M is the midpoint of AB and P is the midpoint of AM.
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4. The product of three negative numbers.
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Decide whether each conjecture is true or false. If false, find a counterexample.
5. The quotient of two whole numbers is a whole number.
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6. The square root of a number x is always less than x.
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7. If a ray intersects a segment at its midpoint, then the ray is perpendicular to the segment.
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Determine if Statement 3 follows from the Statements 1 and 2 by either the Law of Detachment or Law of
Syllogism. If it does, state which law was used. If it does not, write invalid.
8. (1) If an angle measures more than 90°, then it is not acute.
(2) 𝑚∠𝐴𝐵𝐶 = 120°
(3) ∠𝐴𝐵𝐶 is not acute.
9. (1)All 45° angles are congruent.
(2) ∠𝐴 ≅ ∠𝐵
(3) ∠𝐴 and ∠𝐵 are 45°angles.
10. (1)If ∠2 is acute, then ∠3 is obtuse.
(2) If ∠3 is obtuse, then ∠4 is acute.
(3) If ∠2 is acute, then ∠4 is acute.
Make a valid conclusion based on the given statements if possible. If a conclusion can be drawn, then name the
law of logic that was applied.
11. If you order the apple pie, then it will be served with ice cream. Matthew ordered the apple pie.
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12. If you wear the school colors, then you have school spirit. If you have school spirit, then the team feels great.
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13. If you eat too much turkey, then you will get sick. Kinsley got sick.
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14. If an angle is not right, then its measure is between 90° and 180°. A is not right.
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Determine whether or not the given conditional and its converse are true. Use this information to write a
biconditional statement if it is appropriate. If not, explain why it is not appropriate.
15. If it is Wednesday, then it is not Thursday.
Is conditional true or false? ___________________ , Is converse true or false? ___________________
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16. If two lines intersect to form a right angle, then they are perpendicular.
Is conditional true or false? ___________________ , Is converse true or false? ___________________
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Write the biconditional as a conditional and its converse. Then determine whether the biconditional is true or
false. If false, give a counterexample.
17. Two angles are supplementary if and only if the sum of their measures is 180°.
Conditional:______________________________________________________________________________________
Converse:_______________________________________________________________________________________
Is biconditional true or false? _________________
Counter example (if needed):
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Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional.
If the converse is false, provide a counterexample.
18. Complementary angles are two angles whose measures sum up to 90°.
Conditional:______________________________________________________________________________________
Converse: _______________________________________________________________________________________
Biconditional or Counterexample:
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Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional.
If the converse is false, provide a counterexample.
19. Vertical angles are congruent.
Conditional: _____________________________________________________________________________________
Converse: _______________________________________________________________________________________
Biconditional or Counterexample:
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