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5.) Write a conjecture using the information provided below. If someone is 18 years old, he or she can vote. Your cousin can vote. 6.) Write a conjecture using this information. Rectangles are parallelograms. The opposite sides of parallelograms are parallel.

5.) Write a conjecture using the information provided below. If someone is 18 years old, he or she can vote. Your cousin can vote. 6.) Write a conjecture using this information. Rectangles are parallelograms. The opposite sides of parallelograms are parallel.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Conjecture Writing Activity** **Question 5:** Write a conjecture using the information provided below. **Given Information:** - If someone is 18 years old, he or she can vote. - Your cousin can vote. **Your Task:** Using the information provided above, formulate a logical conjecture. --- **Question 6:** Write a conjecture using the information provided below. **Given Information:** - Rectangles are parallelograms. - The opposite sides of parallelograms are parallel. **Your Task:** Using the information provided above, formulate a logical conjecture. --- *Explanation for Students:* A conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. In these exercises, you are given certain pieces of information (facts) and asked to derive a logical conjecture from them. Writing conjectures helps you practice logical thinking and reasoning, which are critical skills in mathematics and science.
Transcribed Image Text:**Conjecture Writing Activity** **Question 5:** Write a conjecture using the information provided below. **Given Information:** - If someone is 18 years old, he or she can vote. - Your cousin can vote. **Your Task:** Using the information provided above, formulate a logical conjecture. --- **Question 6:** Write a conjecture using the information provided below. **Given Information:** - Rectangles are parallelograms. - The opposite sides of parallelograms are parallel. **Your Task:** Using the information provided above, formulate a logical conjecture. --- *Explanation for Students:* A conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. In these exercises, you are given certain pieces of information (facts) and asked to derive a logical conjecture from them. Writing conjectures helps you practice logical thinking and reasoning, which are critical skills in mathematics and science.
Certainly! Here's a transcription and explanation suitable for an educational website: --- ### Exercise: Formulating Conjectures **7. Write a conjecture using the information provided.** **Information:** - If an angle is acute, it cannot be obtuse. - Angle A is obtuse. **Conjecture:** --- **8. Write a conjecture using the information provided.** **Information:** - If two numbers are odd, then their sum is even. - The two numbers are 3 and 19. **Conjecture:** --- **Explanation:** - The exercises feature sections where students are asked to write conjectures based on given statements. - **7.** The information provided states a logical relationship between acute and obtuse angles. Specifically, an angle cannot be both acute and obtuse at the same time, and it specifies that Angle A is obtuse. From this, students are expected to derive a logical conclusion, or conjecture. - **8.** The second part presents a principle in number theory, asserting that the sum of any two odd numbers is even. It then provides two specific odd numbers (3 and 19) for which students must form a conjecture based on this principle. --- This exercise aims to practice forming logical conclusions or hypotheses (conjectures) based on given premises, which is a fundamental skill in both mathematics and logical reasoning.
Transcribed Image Text:Certainly! Here's a transcription and explanation suitable for an educational website: --- ### Exercise: Formulating Conjectures **7. Write a conjecture using the information provided.** **Information:** - If an angle is acute, it cannot be obtuse. - Angle A is obtuse. **Conjecture:** --- **8. Write a conjecture using the information provided.** **Information:** - If two numbers are odd, then their sum is even. - The two numbers are 3 and 19. **Conjecture:** --- **Explanation:** - The exercises feature sections where students are asked to write conjectures based on given statements. - **7.** The information provided states a logical relationship between acute and obtuse angles. Specifically, an angle cannot be both acute and obtuse at the same time, and it specifies that Angle A is obtuse. From this, students are expected to derive a logical conclusion, or conjecture. - **8.** The second part presents a principle in number theory, asserting that the sum of any two odd numbers is even. It then provides two specific odd numbers (3 and 19) for which students must form a conjecture based on this principle. --- This exercise aims to practice forming logical conclusions or hypotheses (conjectures) based on given premises, which is a fundamental skill in both mathematics and logical reasoning.
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