Geometry 2-4 Complete Lesson: Deductive Reasoning

By Matt Richardson
Last updated almost 3 years ago
20 Questions

Solve It! You want to use the coupon to buy three different pairs of jeans. You have narrowed your choices to four pairs. The costs of the different pairs are $24.99, $39.99, $40.99, and $50.00.

If you spend as little as possible, what is the average amount per pair of jeans that you will pay? Explain.

Take Note: Summarize the Law of Detachment.

Problem 1 Got It?

Problem 1 Got It?

Take Note: Summarize the Law of Syllogism.

Problem 2 Got It? What can you conclude from the given information? What is your reasoning?

If a whole number ends in 0, then it is divisible by 10.
If a whole number is divisible by 10, then it is divisible by 5.

Problem 2 Got It? What can you conclude from the given information? What is your reasoning?

If ray AB and ray AD are opposite rays, then the two rays form a straight angle.
If two rays are opposite rays, then the two rays form a straight angle.

Problem 3 Got It? What can you conclude from the given information? What is your reasoning?

If a river is more than 4000 mi long, then it is longer than the Amazon.
If a river is longer than the Amazon, then it is the longest river in the world.
The Nile is 4132 mi long.

Review Lesson 2-3: Write the following definition as a biconditional:

Inductive reasoning is reasoning based on patterns you observe.

Review Lessons 1-4 and 1-5: Use the figure below to respond to the prompts in the right column with items from the left.
You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

  • \angle{O}
  • \angle{COB}
  • \angle{AOB}
  • \overrightarrow{OB}
  • \angle{BOA}
  • obtuse
  • \angle{AOC}
  • acute
  • \angle{BOC}
  • Name ∠1 in two other ways.
  • Name ∠2 in two other ways.
  • If ∠1 ≅ ∠2, name the bisector of ∠AOC.
  • Classify ∠AOC. (acute or obtuse)

Vocabulary Review: Write the converse of the conditional.

If I am thirsty, then I drink water.

Vocabulary Review: Write the inverse of the conditional.

If I am thirsty, then I drink water.

Vocabulary Review: Write the contrapositive of the conditional.

If I am thirsty, then I drink water.

Use Your Vocabulary: Complete each statement on the right with a word from the left.

  • deductive
  • deduction
  • deduce
  • You use __?__ reasoning to draw a conclusion based on facts.
  • The conclusion of your reasoning is a __?__.
  • The teacher will not __?__ that a dog ate your homework.

Reflection: Math Success