1. explain the difference between a drawing and a construction.
2. draw a ray with endpoint a that also contains point b.
3. draw and label a parallelogram that has an area of 24 square inches.
4. compare and contrast lines and rays.
find the next three terms of each sequence.
5. 1,2,4,7,...
6. -800,400,-200,100,...
7. 11,15,19,23,...
for exercises 8 - 11, refer to the figure at the right.
8. name the intersection of $overline{ab}$ and $overline{cd}$.
9. name the intersection of plane $mathcal{i}$ and plane $mathcal{l}$.
10. name a point that is coplanar with points a and e.
11. name three collinear points.
determine whether each statement is true or false. if false, replace the underlined word(s) to make a true statement.
12. the intersection of two planes is a point. 13. two points determine a line.
14. a line segment has two endpoints.
15. three collinear points determine a plane.
write the converse of each statement. then determine whether the converse is true or false. if false, give a counterexample.
16. if $x = 3$, then $x + 10 = 13$.
17. the sum of two odd numbers is an even number.
18. if you live in vermont, then you live in the united states.
use a straightedge or compass to answer each question.
19. is the segment from a to b as long as the segment from c to d?
20. which is longer, pencil l or r?
find the perimeter and area of each rectangle described.
21. $ell = 5$ mm, $w = 12$ mm
22. $ell = 22$ ft, $w = 3$ ft
23. $ell = 16$ m, $w = 14.25$ m
24. find the area of a parallelogram with base 15 feet and height 10 feet.
25. agriculture a sod farmer wants to fertilize and seed a rectangular plot of land 150 feet by 240 feet. a bag of fertilizer covers 5000 square feet, and a bag of grass seed covers 3000 square feet. how many bags of each does the farmer need to buy for this plot of land?

Question

Accepted Answer

1.
# Brief Explanations:
A drawing is a free - hand or approximate representation. A construction is a precise geometric creation using tools like a compass and straightedge following specific geometric rules.
# Answer:
A drawing is an approximate or free - hand representation. A construction is a precise geometric creation using specific tools and rules.

2.
# Brief Explanations:
Place the tip of a straightedge at point A. Then draw a line passing through point B extending infinitely in one direction from A.
# Answer:
Use a straightedge to draw a line starting at A and passing through B, extending infinitely in one direction from A.

3.
# Brief Explanations:
Since the area of a parallelogram is $A = bh$, if $A=24$ square inches, we can choose $b = 6$ inches and $h = 4$ inches. Draw a parallelogram with base 6 inches and height 4 inches and label it.
# Answer:
Draw a parallelogram with base $b = 6$ inches and height $h = 4$ inches and label the sides and height.

4.
# Brief Explanations:
Lines extend infinitely in both directions. Rays have one endpoint and extend infinitely in one direction.
# Answer:
Lines extend infinitely in both directions; rays have one endpoint and extend infinitely in one direction.

5.
# Explanation:
## Step1: Find the pattern
The differences between consecutive terms are 1, 2, 3, and so on.
The difference between the $n$th and $(n + 1)$th term is $n$.
## Step2: Find the next term
The difference between 7 and the next term is 4. So the next term is $7+4 = 11$.
## Step3: Find the second - next term
The difference between 11 and the term after it is 5. So it is $11 + 5=16$.
## Step4: Find the third - next term
The difference between 16 and the term after it is 6. So it is $16+6 = 22$.
# Answer:
11, 16, 22

6.
# Explanation:
## Step1: Find the common ratio
$r=\frac{400}{- 800}=-\frac{1}{2}$
## Step2: Find the next term
$100\times(-\frac{1}{2})=-50$
## Step3: Find the second - next term
$-50\times(-\frac{1}{2}) = 25$
## Step4: Find the third - next term
$25\times(-\frac{1}{2})=-\frac{25}{2}=-12.5$
# Answer:
-50, 25, -12.5

7.
# Explanation:
## Step1: Find the common difference
$d=15 - 11=4$
## Step2: Find the next term
$23+4 = 27$
## Step3: Find the second - next term
$27+4=31$
## Step4: Find the third - next term
$31+4 = 35$
# Answer:
27, 31, 35

8.
# Brief Explanations:
If $\overline{AB}$ and $\overline{CD}$ intersect, we need to look at the point where they cross. But without the figure, assume they are non - parallel lines in the plane of the figure. If they intersect, the intersection is a point.
# Answer:
The intersection point (name it based on the figure, if given).

9.
# Brief Explanations:
The intersection of two planes is a line. We need to identify the line where plane $J$ and plane $L$ meet in the figure.
# Answer:
The line of intersection of plane $J$ and plane $L$ (name it based on the figure, if given).

10.
# Brief Explanations:
Points that lie on the same plane are coplanar. Look for a point in the same plane as $A$ and $E$ in the figure.
# Answer:
A point in the same plane as $A$ and $E$ (name it based on the figure, if given).

11.
# Brief Explanations:
Collinear points lie on the same line. Look for three points on a single line in the figure.
# Answer:
Three points on the same line (name them based on the figure, if given).

12.
# Brief Explanations:
The intersection of two planes is a line, not a point.
# Answer:
False. The intersection of two planes is a line.

13.
# Brief Explanations:
By the postulate, two points determine a unique line.
# Answer:
True

14.
# Brief Explanations:
A line segment is defined as a part of a line with two endpoints.
# Answer:
True

15.
# Brief Explanations:
Three non - collinear points determine a plane. Three collinear points do not determine a unique plane.
# Answer:
False. Three non - collinear points determine a plane.

16.
# Brief Explanations:
The converse of "If $x = 3$, then $x + 10=13$" is "If $x + 10 = 13$, then $x = 3$".
To check if it's true, solve $x+10 = 13$ for $x$ (subtract 10 from both sides: $x=13 - 10=3$).
# Answer:
Converse: If $x + 10 = 13$, then $x = 3$. True.

17.
# Brief Explanations:
The converse of "The sum of two odd numbers is an even number" is "If a number is even, then it is the sum of two odd numbers".
Counter - example: 4 is even, but $4=2 + 2$ where 2 is not odd.
# Answer:
Converse: If a number is even, then it is the sum of two odd numbers. False. Counter - example: 4 is even, $4 = 2+2$ (2 is not odd).

18.
# Brief Explanations:
The converse of "If you live in Vermont, then you live in the United States" is "If you live in the United States, then you live in Vermont".
Counter - example: A person can live in California (in the US) but not in Vermont.
# Answer:
Converse: If you live in the United States, then you live in Vermont. False. Counter - example: A person can live in California (in the US) but not in Vermont.

19.
# Brief Explanations:
Use a straightedge to measure the lengths of $\overline{AB}$ and $\overline{CD}$ and compare them.
# Answer:
Measure $\overline{AB}$ and $\overline{CD}$ with a straightedge to compare their lengths.

20.
# Brief Explanations:
Use a straightedge to measure the lengths of pencil $L$ and pencil $R$ and compare them.
# Answer:
Measure pencil $L$ and pencil $R$ with a straightedge to determine which is longer.

21.
# Explanation:
## Step1: Calculate the perimeter of the rectangle
The formula for the perimeter of a rectangle is $P=2(l + w)$. Given $l = 5$ mm and $w = 12$ mm, $P=2(5 + 12)=2\times17 = 34$ mm.
## Step2: Calculate the area of the rectangle
The formula for the area of a rectangle is $A=lw$. So $A=5\times12 = 60$ $mm^{2}$.
# Answer:
Perimeter: 34 mm; Area: 60 $mm^{2}$

22.
# Explanation:
## Step1: Calculate the perimeter of the rectangle
$P=2(l + w)$, with $l = 22$ ft and $w = 3$ ft. $P=2(22+3)=2\times25 = 50$ ft.
## Step2: Calculate the area of the rectangle
$A=lw$, so $A=22\times3=66$ $ft^{2}$.
# Answer:
Perimeter: 50 ft; Area: 66 $ft^{2}$

23.
# Explanation:
## Step1: Calculate the perimeter of the rectangle
$P=2(l + w)$, with $l = 16$ m and $w = 14.25$ m. $P=2(16 + 14.25)=2\times30.25 = 60.5$ m.
## Step2: Calculate the area of the rectangle
$A=lw$, so $A=16\times14.25 = 228$ $m^{2}$.
# Answer:
Perimeter: 60.5 m; Area: 228 $m^{2}$

24.
# Explanation:
## Step1: Use the area formula for a parallelogram
The formula for the area of a parallelogram is $A = bh$. Given $b = 15$ feet and $h = 10$ feet, $A=15\times10=150$ square feet.
# Answer:
150 square feet

25.
# Explanation:
## Step1: Calculate the area of the rectangular plot
The area of the rectangle is $A=lw$, with $l = 240$ feet and $w = 150$ feet. So $A=240\times150 = 36000$ square feet.
## Step2: Calculate the number of fertilizer bags
The number of fertilizer bags $n_{1}=\frac{36000}{5000}=7.2$. Since we can't buy a fraction of a bag, we need 8 bags of fertilizer.
## Step3: Calculate the number of grass - seed bags
The number of grass - seed bags $n_{2}=\frac{36000}{3000}=12$ bags.
# Answer:
8 bags of fertilizer; 12 bags of grass - seed.

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