Geometry worksheet focusing on conditional statements, including identifying hypotheses and conclusions, writing syllogisms, and determining truth values of conditional statements.
Geometry 2.1 - 2.3 Conditionals Worksheet with exercises on hypothesis and conclusion, syllogisms, and conditional statements.
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Step-by-step solution for: 2.1-2.3 WS Conditionals | PDF | Angle | Geometry
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Show Answer Key & Explanations
Step-by-step solution for: 2.1-2.3 WS Conditionals | PDF | Angle | Geometry
Let's go through each section of the Geometry: 2.1 – 2.3 Conditionals Worksheet step by step, solving and explaining each problem.
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We identify the hypothesis (the "if" part) and the conclusion (the "then" part) in each conditional statement.
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1. If you are funny, then you will make people laugh.
- Hypothesis: You are funny
- Conclusion: You will make people laugh
> ✔ This is a standard if-then structure.
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2. If a point is in the interior of an angle, then it cannot be in its exterior.
- Hypothesis: A point is in the interior of an angle
- Conclusion: It cannot be in its exterior
> ✔ The "if" part is the condition; the "then" part is the result.
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3. If A is between B and C, then A, B, and C are collinear.
- Hypothesis: A is between B and C
- Conclusion: A, B, and C are collinear
> ✔ In geometry, "between" implies they lie on a straight line → collinear.
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This involves logical reasoning using transitivity:
If P → Q and Q → R, then P → R.
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4a.
- If a fish weighs over 2000 lbs, then it is the largest species of fish.
- If a fish is the largest species of fish, then it is a great white shark.
Chain:
Weight > 2000 lbs → Largest species → Great white shark
So, combining:
> If a fish weighs over 2000 lbs, then it is a great white shark.
✔ This is the logical conclusion via transitive reasoning.
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4b.
- If John visits Greensboro, then he will go to Emerald Point.
- If John goes to Emerald Point, then he will swim.
Chain:
Visits Greensboro → Goes to Emerald Point → Will swim
So:
> If John visits Greensboro, then he will swim.
✔ Again, transitive logic applies.
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We form a proper "if-then" statement from the given parts.
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5.
- Hypothesis: A number is prime
- Conclusion: The number has exactly two divisors
→ If a number is prime, then it has exactly two divisors.
✔ This is a definition of a prime number.
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6.
- Hypothesis: Four points are in one plane
- Conclusion: The points are coplanar
→ If four points are in one plane, then the points are coplanar.
✔ Note: "Coplanar" means lying in the same plane — so this is a tautology, but still valid.
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7.
- Hypothesis: A man lives in Houston
- Conclusion: He lives in Texas
→ If a man lives in Houston, then he lives in Texas.
✔ Since Houston is in Texas, this is logically sound.
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We rewrite each as "If..., then..." and assess truth value.
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8. A line which bisects a segment contains the midpoint of the segment.
→ If a line bisects a segment, then it contains the midpoint of the segment.
✔ True.
By definition, a bisector divides a segment into two equal parts, and that only happens if it passes through the midpoint.
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9. Collinear points are points that lie on the same line.
→ If points are collinear, then they lie on the same line.
✔ True.
This is the definition of collinear points.
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10. All left-handed people are male.
→ If a person is left-handed, then they are male.
✘ False.
This is not true — many left-handed people are female. The statement generalizes incorrectly.
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11. All acute angles are congruent.
→ If an angle is acute, then it is congruent to all other acute angles.
✘ False.
Acute angles are less than 90°, but they can have different measures (e.g., 30° vs 60°), so they are not necessarily congruent.
> Congruent means equal in measure — not all acute angles are equal.
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#### I. Hypothesis and Conclusion
1.
- Hypothesis: You are funny
- Conclusion: You will make people laugh
2.
- Hypothesis: A point is in the interior of an angle
- Conclusion: It cannot be in its exterior
3.
- Hypothesis: A is between B and C
- Conclusion: A, B, and C are collinear
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#### II. Syllogisms
4a. If a fish weighs over 2000 lbs, then it is a great white shark.
4b. If John visits Greensboro, then he will swim.
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#### III. Conditional Statements
5. If a number is prime, then it has exactly two divisors.
6. If four points are in one plane, then the points are coplanar.
7. If a man lives in Houston, then he lives in Texas.
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#### IV. Rewrite & Truth Value
8. If a line bisects a segment, then it contains the midpoint of the segment. → True
9. If points are collinear, then they lie on the same line. → True
10. If a person is left-handed, then they are male. → False
11. If an angle is acute, then it is congruent to all other acute angles. → False
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Let me know if you'd like this formatted as a printable answer key!
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I. State the hypothesis and conclusion for each statement.
We identify the hypothesis (the "if" part) and the conclusion (the "then" part) in each conditional statement.
---
1. If you are funny, then you will make people laugh.
- Hypothesis: You are funny
- Conclusion: You will make people laugh
> ✔ This is a standard if-then structure.
---
2. If a point is in the interior of an angle, then it cannot be in its exterior.
- Hypothesis: A point is in the interior of an angle
- Conclusion: It cannot be in its exterior
> ✔ The "if" part is the condition; the "then" part is the result.
---
3. If A is between B and C, then A, B, and C are collinear.
- Hypothesis: A is between B and C
- Conclusion: A, B, and C are collinear
> ✔ In geometry, "between" implies they lie on a straight line → collinear.
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II. Assume the statements are true. Write the conclusion of each syllogism (in “if-then” form).
This involves logical reasoning using transitivity:
If P → Q and Q → R, then P → R.
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4a.
- If a fish weighs over 2000 lbs, then it is the largest species of fish.
- If a fish is the largest species of fish, then it is a great white shark.
Chain:
Weight > 2000 lbs → Largest species → Great white shark
So, combining:
> If a fish weighs over 2000 lbs, then it is a great white shark.
✔ This is the logical conclusion via transitive reasoning.
---
4b.
- If John visits Greensboro, then he will go to Emerald Point.
- If John goes to Emerald Point, then he will swim.
Chain:
Visits Greensboro → Goes to Emerald Point → Will swim
So:
> If John visits Greensboro, then he will swim.
✔ Again, transitive logic applies.
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III. Write a conditional with the given hypothesis and conclusion.
We form a proper "if-then" statement from the given parts.
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5.
- Hypothesis: A number is prime
- Conclusion: The number has exactly two divisors
→ If a number is prime, then it has exactly two divisors.
✔ This is a definition of a prime number.
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6.
- Hypothesis: Four points are in one plane
- Conclusion: The points are coplanar
→ If four points are in one plane, then the points are coplanar.
✔ Note: "Coplanar" means lying in the same plane — so this is a tautology, but still valid.
---
7.
- Hypothesis: A man lives in Houston
- Conclusion: He lives in Texas
→ If a man lives in Houston, then he lives in Texas.
✔ Since Houston is in Texas, this is logically sound.
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IV. Write each statement as a conditional. Then determine if it is true or false.
We rewrite each as "If..., then..." and assess truth value.
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8. A line which bisects a segment contains the midpoint of the segment.
→ If a line bisects a segment, then it contains the midpoint of the segment.
✔ True.
By definition, a bisector divides a segment into two equal parts, and that only happens if it passes through the midpoint.
---
9. Collinear points are points that lie on the same line.
→ If points are collinear, then they lie on the same line.
✔ True.
This is the definition of collinear points.
---
10. All left-handed people are male.
→ If a person is left-handed, then they are male.
✘ False.
This is not true — many left-handed people are female. The statement generalizes incorrectly.
---
11. All acute angles are congruent.
→ If an angle is acute, then it is congruent to all other acute angles.
✘ False.
Acute angles are less than 90°, but they can have different measures (e.g., 30° vs 60°), so they are not necessarily congruent.
> Congruent means equal in measure — not all acute angles are equal.
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✔ Final Answers Summary:
#### I. Hypothesis and Conclusion
1.
- Hypothesis: You are funny
- Conclusion: You will make people laugh
2.
- Hypothesis: A point is in the interior of an angle
- Conclusion: It cannot be in its exterior
3.
- Hypothesis: A is between B and C
- Conclusion: A, B, and C are collinear
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#### II. Syllogisms
4a. If a fish weighs over 2000 lbs, then it is a great white shark.
4b. If John visits Greensboro, then he will swim.
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#### III. Conditional Statements
5. If a number is prime, then it has exactly two divisors.
6. If four points are in one plane, then the points are coplanar.
7. If a man lives in Houston, then he lives in Texas.
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#### IV. Rewrite & Truth Value
8. If a line bisects a segment, then it contains the midpoint of the segment. → True
9. If points are collinear, then they lie on the same line. → True
10. If a person is left-handed, then they are male. → False
11. If an angle is acute, then it is congruent to all other acute angles. → False
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Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of geometry conditional statements worksheet with answers.
