Geometry 2.2 Inductive/Deductive Reasoning

Find the pattern in the sequence below. Write the next two numbers in the sequence.

2, 5, 11, 23, 47, ...

Find the pattern in the sequence below. Write the next two letters in the sequence.

A, Z, B, Y, C, ...

Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion.

This weekend, the sun was shining and it did not rain. So, the next time the sun is shining, you know it will not rain.​ (a)  

• Inductive
• Deductive

Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion.

The product of two even integers is always even. Because 92 and 14 are even numbers, the product is even.​ (a)  

• Deductive
• Inductive

The three tallest peaks in the Rocky Mountains are 4401 meters, 4398 meters, and 4396 meters. The three tallest peaks in the Appalachian Mountains are 2037 meters, 2026 meters, and 2025 meters. Which of the following could be a conjecture made that compares the Rocky Mountains to the Appalachian Mountains?

• People like the Appalachian Mts. better than the Rocky mts.

• The Rocky Mts. are taller than the Appalachian Mts.

• The Appalachian Mts. are taller than the Rocky Mts.

• Both mountain ranges are about the same height.

Use deductive reasoning to write a formula for the perimeter P of a regular polygon with n sides, where each side is s.

• ps = n

• pn = s

• s = pn

• p = ns

If |x| = x , then x is positive. The value of x is 3, so |3| = 3.
State the law of logic that is illustrated.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• not true
• true

Write the logical argument symbolically.

If a straight angle is bisected, then each new angle measures 90. If an angle measures 90, then the angle is a right angle. Ryan bisects a straight angle. Therefore, the new angles are right angles.

​ (a)   ​ ​ (b)   . ​ (c)   is true.​ ​ (d)   the statement is ​ (e)  

• not true
• true
• p

• not true
• true
• p