Question

(from unit 2, lesson 2)

1. each table represents a proportional relationship. for each table:

a. fill in the missing parts of the table.
b. draw a circle around the constant of proportionality.

(from unit 2, lesson 2)

1. describe some things you could notice in two polygons that would help you decide that they were scaled copies.

(from unit 1, lesson 4)

Explanation:

Step1: Find the constant of proportionality for the first table

For a proportional relationship $y = kx$, using the first - row values $x = 2$ and $y = 10$, we find $k=\frac{y}{x}=\frac{10}{2}=5$.

Step2: Fill in the missing values for the first table

When $y = 15$, then $x=\frac{y}{k}=\frac{15}{5}=3$. When $x = 7$, then $y=kx = 5\times7 = 35$. When $x = 1$, then $y=kx=5\times1 = 5$.

Step3: Find the constant of proportionality for the second table

For the relationship $b = ka$, using the first - row values $a = 12$ and $b = 3$, we find $k=\frac{b}{a}=\frac{3}{12}=\frac{1}{4}$.

Step4: Fill in the missing values for the second table

When $a = 20$, then $b=ka=\frac{1}{4}\times20 = 5$. When $b = 10$, then $a=\frac{b}{k}=\frac{10}{\frac{1}{4}}=40$. When $a = 1$, then $b=ka=\frac{1}{4}\times1=\frac{1}{4}$.

Step5: Find the constant of proportionality for the third table

For the relationship $n = km$, using the first - row values $m = 5$ and $n = 3$, we find $k=\frac{n}{m}=\frac{3}{5}=0.6$.

Step6: Fill in the missing values for the third table

When $m = 10$, then $n=km=0.6\times10 = 6$. When $n = 18$, then $m=\frac{n}{k}=\frac{18}{0.6}=30$. When $m = 1$, then $n=km=0.6\times1 = 0.6$.

For the second part of the problem (question 6):

If two polygons are scaled copies, the corresponding angles are equal, and the ratios of the corresponding side - lengths are equal.

Answer:

For the tables:
Table 1:

x	y
3	15
7	35
1	5

Constant of proportionality is 5.

Table 2:

a	b
20	5
40	10
1	$\frac{1}{4}$

Constant of proportionality is $\frac{1}{4}$.

Table 3:

m	n
10	6
30	18
1	0.6

Constant of proportionality is 0.6.

For question 6: Corresponding angles are equal and ratios of corresponding side - lengths are equal.