Question

lesson 3 - 2
for items 8 - 10, write each statement in if - then form.

1. dianna will go to the movie if she finishes her homework.
2. (mangle g = 40^{circ}) implies (angle g) is acute.
3. a figure is a triangle only if it is a polygon with three sides.
4. state the hypothesis and the conclusion of this conditional statement.

if the temperature drops below (65^{circ}f), then the swimming pool closes.

1. given the false conditional statement, “if a vehicle is built to fly, then it is an airplane,” write a counterexample.
2. dustin says that (8cdot - 1 = 8) is a counterexample that shows that the following conditional statement is false. is dustin correct? explain.

if two integers are multiplied, then the product is greater than both integers.

1. given that the hypothesis of the following conditional statement is true, which statement must also be true?

if margo wears gloves or a scarf, then she wears a coat.
a. margo is wearing a coat.
b. margo is wearing gloves.
c. margo is not wearing a coat.
d. margo is not wearing gloves.

1. a. write a true conditional statement that includes this hypothesis: (-3x + 10=-5).

b. write a two - column proof to prove that your conditional statement is true.

Explanation:

Step1: Rewrite statements in if - then form

1. If Dianna finishes her homework, then she will go to the movie.
2. If \(m\angle G = 40^{\circ}\), then \(\angle G\) is acute.
3. If a figure is a triangle, then it is a polygon with three sides.

Step2: Identify hypothesis and conclusion

1. Hypothesis: The temperature drops below \(65^{\circ}F\). Conclusion: The swimming pool closes.

Step3: Find counter - example

1. A helicopter is a vehicle built to fly but it is not an airplane.

Step4: Analyze counter - example

1. Dustin is correct. Since \(8\times(- 1)=-8

eq8\), and \(-8<8\), it shows that the product of two integers is not always greater than both integers.

Step5: Determine true statement

1. If the hypothesis “Margo wears gloves or a scarf” is true, then by the conditional statement “If Margo wears gloves or a scarf, then she wears a coat”, Margo is wearing a coat. So the answer is A. Margo is wearing a coat.

Step6: Write conditional statement and proof

1. a. If \(-3x + 10=-5\), then \(x = 5\).

b.

Statements	Reasons
\(-3x=-5 - 10\)	Subtraction Property of Equality
\(-3x=-15\)	Simplify
\(x = 5\)	Division Property of Equality

Answer:

1. If Dianna finishes her homework, then she will go to the movie.
2. If \(m\angle G = 40^{\circ}\), then \(\angle G\) is acute.
3. If a figure is a triangle, then it is a polygon with three sides.
4. Hypothesis: The temperature drops below \(65^{\circ}F\). Conclusion: The swimming pool closes.
5. A helicopter is a vehicle built to fly but it is not an airplane.
6. Dustin is correct. Since \(8\times(-1)=-8

eq8\), and \(-8 < 8\), it shows that the product of two integers is not always greater than both integers.

1. A. Margo is wearing a coat.
2. a. If \(-3x + 10=-5\), then \(x = 5\).

b. See the two - column proof above.