Name:___________________________Period:_____________________Date:________________
Unit 1: Lesson 1 and 2 PRACTICE Quiz – Reasoning and Proof
Directions: Show your statements, reasons, and work logically. Be sure to explain everything.
1. “All registered voters in the United States are at least 18 years old.”
a. Rewrite the statement in if-then form.
b. Evan lives in Iowa and is 20 years old. What can you conclude?
c. Brittany lives in Virginia and is registered to vote. What can you conclude?
2. A class of students at Jasper High School was asked to prove the following conjecture.
If you double the length of a rectangle (and do not change the width), then the area of the rectangle
doubles.
Consider each argument below and decide if it is a correct proof. Explain your reasoning.
a. Levi’s:
b. Julian’s:
c. What might be added to the argument in Part b to make it easier to follow.
3. If two angles are supplementary, then the sum of their measures is 180 and complementary if
the sum of their measures is 90 .
a. Suppose you know that A and B are supplementary and that mB  80 . What can
you conclude?
b. Suppose that mC  145 . Is it possible that C and
convincing argument to support your answer
4. If a and b are odd then a 2  b 2 is even.
a. Check this using inductive reasoning.
b. Give a deductive proof.
5. If n is even then n 2 is even.
a. Check this using inductive reasoning.
b. Give a deductive proof.
D are complementary? Provide a