Set of engaging math worksheets covering similar polygons, circumference, scale drawings, and circle vocabulary, designed for interactive learning.

Here are the solutions for the math problems shown on the worksheets. I have broken them down by activity type so you can check your work easily.

1. Similar Polygons (Partner Activity)

*Goal: Find the missing side length $x$ using proportions.*

Column A Problems:
* Trapezoids: The ratio of the top sides is $\frac{8}{24}$, which simplifies to $\frac{1}{3}$. To find $x$ (the bottom side), multiply the corresponding bottom side by 3:
$$6 \times 3 = 18$$
Answer: $x = 18$ m

* Rectangles: The vertical sides give us the scale factor: $\frac{26}{39} = \frac{2}{3}$. To find $x$ (the top horizontal side), multiply the larger rectangle's width by $\frac{2}{3}$:
$$81 \times \frac{2}{3} = 54$$
Answer: $x = 54$ m

* Triangles: Compare the long slanted sides: $\frac{42}{105} = 0.4$ (or $\frac{2}{5}$). To find $x$ (the short slanted side), multiply the smaller triangle's base by the inverse scale factor ($\frac{105}{42} = 2.5$):
$$15 \times 2.5 = 37.5$$
Answer: $x = 37.5$ m

*(Note: In a partner activity, Column B would yield these same answers.)*

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2. Scale Drawings (Math Maze)

*Goal: Solve the proportion to find the actual distance and follow the correct path.*

1. Town A to Town B:
* Scale: $1 \text{ cm} = 5 \text{ miles}$. Map distance: $15 \text{ cm}$.
* Calculation: $15 \times 5 = 75$.
* Correct Path Answer: 75 mi

2. Store to Kim's House:
* Scale: $1 \text{ inch} = 3.2 \text{ miles}$. Map distance: $13 \text{ inches}$.
* Calculation: $13 \times 3.2 = 41.6$.
* Correct Path Answer: 41.6 mi

3. Vase Drawing:
* Scale: $1 \text{ cm} = 0.5 \text{ inches}$. Actual height: $24 \text{ inches}$.
* Calculation: $24 \times 0.5 = 12$.
* Correct Path Answer: 12 cm

4. Town C to Town D:
* Scale: $1 \text{ inch} = \frac{1}{4} \text{ mile}$ (which is $0.25$). Map distance: $3\frac{1}{2}$ inches ($3.5$).
* Calculation: $3.5 \times 0.25 = 0.875$. Since $\frac{7}{8} = 0.875$, this matches.
* Correct Path Answer: 7/8 mi

5. Coffee Shop to Mall:
* Scale: $1 \text{ inch} = \frac{3}{4} \text{ miles}$ ($0.75$). Map distance: $\frac{5}{6}$ inches.
* Calculation: $\frac{5}{6} \times \frac{3}{4} = \frac{15}{24}$. Simplify by dividing top and bottom by 3 to get $\frac{5}{8}$.
* Correct Path Answer: 5/8 mi

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3. Circle Vocabulary (Secret Message)

*Goal: Identify the parts of the circle based on the diagrams.*

* #1 Name the circle: The center point is labeled O.
* Answer: B) O
* #2 Specific name for $\overline{OD}$: It connects the center to the edge.
* Answer: D) Radius
* #3 Specific name for $\overline{BA}$: It connects two points on the edge but does not go through the center.
* Answer: E) Chord
* #4 Example of a diameter: A line passing through the center connecting opposite edges. Looking at the second diagram, $\overline{PG}$ fits this description.
* Answer: H) PG
* #5 Example of a radius: Connects center $P$ to the edge. $\overline{JP}$ fits.
* Answer: J) JP
* #6 Example of an arc: A curved part of the circle. $\overarc{FG}$ represents the curve from F to G.
* Answer: K) $\overarc{FG}$
* #7 Example of a semicircle: Half of the circle. In the third diagram, the line divides it in half. $\overarc{JKL}$ is half the circle.
* Answer: N) $\overarc{JKL}$
* #8 Example of a diameter: In the third diagram, $\overline{JL}$ goes through the center.
* Answer: P) JL
* #9 Specific name for $\overline{QM}$: Connects center $Q$ to the edge.
* Answer: R) Radius

*(Shading the boxes with letters B, D, E, H, J, K, N, P, R will reveal the secret message.)*

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4. Circumference (Dice Practice)

*Since this requires rolling dice, here is how you solve it once you have your numbers:*

1. Roll two dice and multiply them. Let's say you rolled a 4 and a 5. Your diameter ($d$) is $20$.
2. Use the formula: $C = \pi \times d$.
3. Calculate: $20 \times 3.14 = 62.8$.

Final Answer:
Similar Polygons: x = 18 m, x = 54 m, x = 37.5 m
Scale Drawings Maze Path: 75 mi → 41.6 mi → 12 cm → 7/8 mi → 5/8 mi
Circle Vocabulary Answers: #1:B, #2:D, #3:E, #4:H, #5:J, #6:K, #7:N, #8:P, #9:R