Learning Target 2
2.3 Deductive Reasoning
2.4 Use Postulates and Diagrams
Name_________________________________________________
Period _______________________
Homework
For problems 1-6, decide whether inductive or deductive reasoning is used to reach the conclusion.
Explain your reasoning.
1. While shopping for a product, you notice that brand A is more expensive than brand B. You
conclude that brand A is of higher quality than brand B.
2. Because the brand A product costs $1.50 and the brand B product costs $1.00, you conclude
that the brand A product is 50% more expensive.
3. It normally takes you 20 minutes to walk home from school. By walking faster one day, you
make it in 15 minutes. The following day, you make it in 12 minutes. You conclude that you
could make the trip in as little as 10 minutes.
4. On the first meet of the year, JD, Bob, and Raul finish their race in a tie. In the final meet of the
year, Raul finishes well ahead of Bob and JD. Having seen both races, you conclude that Raul
trained the hardest.
5. Angela knows that Walt is taller than Peter. She also knows that Peter is taller than Natalie.
Angela reasons that Walt is taller than Natalie.
6. For the past three Wednesdays, the cafeteria has served macaroni and cheese for lunch. Dana
concludes that the cafeteria will serve macaroni and cheese for lunch this Wednesday.
7. Error analysis: Describe and correct the error in the argument: “If two angles are a linear pair,
then they are supplementary. Angles C and D are supplementary, so the angles are a linear pair.”
For problems 8-10, decide whether the statement is true or false. If it is false, five a real-world
counterexample.
8. Through any three points, there exists exactly one line.
9. A point can be in more than one plane.
10. Any two planes intersect.
For problems 11-21, use the diagram to determine if the statement is true or false. Explain your
reasoning.
11. Planes W and X intersect at ⃡𝐾𝐿.
12. Points Q, J, and M are collinear.
13. Points K, L, M and R are coplanar.
14. ⃡𝑀𝑁 and ⃡𝑅𝑃 intersect.
⃡ ⊥ plane W.
15. 𝑅𝑃
16. ⃡𝐽𝐾 lies in plane X.
17. ∠𝑃𝐿𝐾 is a right angle.
18. ∠𝑁𝐾𝐿 and ∠𝐽𝐾𝑀 are vertical angles.
19. ∠𝑁𝐾𝐽 and ∠𝐽𝐾𝑀 are supplementary angles.
20. ∠𝐽𝐾𝑀 and ∠𝐾𝐿𝑃 are congruent angles.
For problems 21 and 22, write out the postulate illustrated by the diagram.
21.
22.
23. Multiple Choice: Which of the following statements cannot be assumed from the diagram?
a) Points A, B, C and E are coplanar
b) Points F, B, and G are collinear
c) ⃡𝐻𝐶 ⊥ ⃡𝐺𝐸
d) ⃡𝐸𝐶 intersects plane M at point C