activity 3 practice
write your answers on notebook paper. show your work.
lesson 3 - 1
1. identify the property that justifies the statement: 5(x - 3)=5x - 15
a. multiplication b. transitive c. subtraction d. distributive
2. a. give an example of an undefined term and a defined term in geometry.
b. explain the difference between an undefined term and a defined term.
3. how is a definition different from a theorem?
4. what are the missing reasons and statements in the two - column proof?
given: $\frac{2x}{4}=\frac{5x + 8}{2}$ prove: $x=-2$
statements reasons
1. a. 1. given equation
2. $2x = 2(5x + 8)$ 2. b.
3. c. 3. distributive property
4. $0 = 8x+16$ 4. d.
5. e. 5. subtraction property of equality
6. $-2=x$ 6. f.
7. g. 7. symmetric property
for items 5 and 6, complete the prove statement and write a two - column proof for the equation.
5. given: $5(x - 2)=2x - 4$ prove:
6. given: $\frac{4c - 6}{3}=8$ prove:
7. suppose you are given that $a = 5$ and $4a + b = 6$. what can you prove by using these statements and the substitution property?
lesson 3 - 2
for items 8 - 10, write each statement in if - then form.
8. dianna will go to the movie if she finishes her homework.
9. $mangle g = 40^{circ}$ implies $angle g$ is acute.
10. a figure is a triangle only if it is a polygon with three sides.
11. state the hypothesis and the conclusion of this conditional statement.
if the temperature drops below $65^{circ}f$, then the swimming pool closes.
12. given the false conditional statement, \if a vehicle is built to fly, then it is an airplane,\ write a counterexample.
13. 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.
14. 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.
15. 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.

Question

activity 3 practice
write your answers on notebook paper. show your work.
lesson 3 - 1
1. identify the property that justifies the statement: 5(x - 3)=5x - 15
a. multiplication b. transitive c. subtraction d. distributive
2. a. give an example of an undefined term and a defined term in geometry.
  b. explain the difference between an undefined term and a defined term.
3. how is a definition different from a theorem?
4. what are the missing reasons and statements in the two - column proof?
given: $\frac{2x}{4}=\frac{5x + 8}{2}$ prove: $x=-2$
statements reasons
1. a. 1. given equation
2. $2x = 2(5x + 8)$ 2. b.
3. c. 3. distributive property
4. $0 = 8x+16$ 4. d.
5. e. 5. subtraction property of equality
6. $-2=x$ 6. f.
7. g. 7. symmetric property
for items 5 and 6, complete the prove statement and write a two - column proof for the equation.
5. given: $5(x - 2)=2x - 4$ prove:
6. given: $\frac{4c - 6}{3}=8$ prove:
7. suppose you are given that $a = 5$ and $4a + b = 6$. what can you prove by using these statements and the substitution property?
lesson 3 - 2
for items 8 - 10, write each statement in if - then form.
8. dianna will go to the movie if she finishes her homework.
9. $mangle g = 40^{circ}$ implies $angle g$ is acute.
10. a figure is a triangle only if it is a polygon with three sides.
11. state the hypothesis and the conclusion of this conditional statement.
if the temperature drops below $65^{circ}f$, then the swimming pool closes.
12. given the false conditional statement, \if a vehicle is built to fly, then it is an airplane,\ write a counterexample.
13. 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.
14. 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.
15. 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.

Accepted Answer

### 1.
# Explanation:
## Step1: Recall distributive property
The distributive property states that $a(b - c)=ab - ac$. Here $a = 5$, $b=x$ and $c = 3$, so $5(x - 3)=5x-15$.
# Answer:
D. distributive

### 2. a.
# Brief Explanations:
In geometry, a point is an undefined - term (it has no formal definition in terms of other geometric concepts). A triangle is a defined term as it is defined as a polygon with three sides.
# Answer:
An example of an undefined term is a point. An example of a defined term is a triangle.

### 2. b.
# Brief Explanations:
An undefined term is a basic building - block of geometry that cannot be defined in simpler terms. A defined term is built from undefined terms and other defined terms using logical definitions.
# Answer:
An undefined term has no formal definition in terms of other geometric concepts, while a defined term is defined using undefined terms and other defined terms.

### 3.
# Brief Explanations:
A definition is a statement that gives the meaning of a term. A theorem is a statement that can be proven using definitions, postulates, and previously - proven theorems.
# Answer:
A definition gives the meaning of a term, while a theorem is a provable statement.

### 4.
# Explanation:
## Step1: Given equation
The first statement is the given equation $\frac{2x}{4}=\frac{5x + 8}{2}$, so a. $\frac{2x}{4}=\frac{5x + 8}{2}$
## Step2: Cross - multiply
Cross - multiplying the given equation gives $2x=2(5x + 8)$, and the reason is Cross - Multiplication Property. So b. Cross - Multiplication Property
## Step3: Expand the right - hand side
Expanding $2(5x + 8)$ using the distributive property gives $2x = 10x+16$, so c. $2x=10x + 16$
## Step4: Subtract $2x$ from both sides
Subtracting $2x$ from both sides of $2x=10x + 16$ gives $0 = 8x+16$, and the reason is Subtraction Property of Equality. So d. Subtraction Property of Equality
## Step5: Subtract 16 from both sides
Subtracting 16 from both sides of $0 = 8x+16$ gives $-16=8x$, so e. $-16 = 8x$
## Step6: Divide both sides by 8
Dividing both sides of $-16 = 8x$ by 8 gives $-2=x$, and the reason is Division Property of Equality. So f. Division Property of Equality
## Step7: Rewrite the equation
Using the symmetric property, we can rewrite $-2=x$ as $x=-2$, so g. $x=-2$
# Answer:
a. $\frac{2x}{4}=\frac{5x + 8}{2}$; b. Cross - Multiplication Property; c. $2x=10x + 16$; d. Subtraction Property of Equality; e. $-16 = 8x$; f. Division Property of Equality; g. $x=-2$

### 8.
# Answer:
If Dianna finishes her homework, then she will go to the movie.

### 9.
# Answer:
If $m\angle G = 40^{\circ}$, then $\angle G$ is acute.

### 10.
# Answer:
If a figure is a triangle, then it is a polygon with three sides.

### 11.
# Answer:
Hypothesis: The temperature drops below $65^{\circ}F$. Conclusion: The swimming pool closes.

### 12.
# Answer:
A counter - example is a helicopter. A helicopter is built to fly but is not an airplane.

### 13.
# Answer:
Dustin is correct. The product of $8$ and $-1$ is $-8$ which is less than $8$. This shows that the statement “If two integers are multiplied, then the product is greater than both integers” is false.

### 14.
# Answer:
A. Margo is wearing a coat. Since the hypothesis “Margo wears gloves or a scarf” is true, by the conditional statement “If Margo wears gloves or a scarf, then she wears a coat”, the conclusion “she wears a coat” must be true.

### 15. a.
# Answer:
If $-3x + 10=-5$, then $x = 5$.

### 15. b.
# Explanation:
## Step1: Given hypothesis
Given $-3x + 10=-5$
## Step2: Subtract 10 from both sides
$-3x+10 - 10=-5 - 10$, which simplifies to $-3x=-15$ (Subtraction Property of Equality)
## Step3: Divide both sides by $-3$
$\frac{-3x}{-3}=\frac{-15}{-3}$, which gives $x = 5$ (Division Property of Equality)
# Answer:
| Statements | Reasons |
|--|--|
| 1. $-3x + 10=-5$ | Given |
| 2. $-3x=-15$ | Subtraction Property of Equality |
| 3. $x = 5$ | Division Property of Equality |

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Recall distributive property

Answer:

2. a.