To solve these problems, we need to use the property of
similar triangles. Similar triangles have the same shape but different sizes. This means their corresponding sides are in proportion (they grow or shrink by the same multiplier).
Here is the step-by-step solution for each pair:
Part A
1.
Find the scale factor: Look at the sides where you know both lengths. The small triangle has a bottom side of
7 cm, and the large triangle has a corresponding bottom side of
10 cm.
* Scale Factor = $10 \div 7 = \frac{10}{7}$ (approx 1.43).
2.
Calculate the missing left side: The small triangle's left side is
4 cm. Multiply this by the scale factor.
* $4 \times \frac{10}{7} = \frac{40}{7} \approx \mathbf{5.71 \text{ cm}}$.
3.
Calculate the missing right side: The small triangle's right side is
5 cm. Multiply this by the scale factor.
* $5 \times \frac{10}{7} = \frac{50}{7} \approx \mathbf{7.14 \text{ cm}}$.
Part B
1.
Find the scale factor: Compare the known corresponding sides. The small triangle has a side of
3 cm, and the large triangle has a corresponding side of
12 cm.
* Scale Factor = $12 \div 3 = \mathbf{4}$. The large triangle is 4 times bigger.
2.
Calculate the missing side: The small triangle has another side of
4 cm. Multiply this by the scale factor.
* $4 \times 4 = \mathbf{16 \text{ cm}}$.
Part C
1.
Find the scale factor: Compare the known corresponding sides. The small triangle has a hypotenuse (longest side) of
5 cm, and the large triangle has a corresponding hypotenuse of
4.5 cm.
* Scale Factor = $4.5 \div 5 = \mathbf{0.9}$. The large triangle is 0.9 times the size of the small one.
2.
Calculate the missing vertical side: The small triangle has a vertical side of
3 cm.
* $3 \times 0.9 = \mathbf{2.7 \text{ cm}}$.
3.
Calculate the missing horizontal side: The small triangle has a horizontal side of
4 cm.
* $4 \times 0.9 = \mathbf{3.6 \text{ cm}}$.
Part D
1.
Find the scale factor: Compare the known corresponding sides. The large triangle has a side of
4 cm, and the small triangle has a corresponding side of
3 cm.
* Scale Factor (Large to Small) = $3 \div 4 = \mathbf{0.75}$.
2.
Calculate the top missing side: The large triangle has a top side of
3 cm.
* $3 \times 0.75 = \mathbf{2.25 \text{ cm}}$.
3.
Calculate the bottom missing side: The large triangle has a bottom side of
2 cm.
* $2 \times 0.75 = \mathbf{1.5 \text{ cm}}$.
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Final Answer:
A: Left box:
5.71 cm (or $\frac{40}{7}$ cm), Bottom box:
7.14 cm (or $\frac{50}{7}$ cm)
B: Box:
16 cm
C: Vertical box:
2.7 cm, Horizontal box:
3.6 cm
D: Top box:
2.25 cm, Bottom box:
1.5 cm
Parent Tip: Review the logic above to help your child master the concept of similarity and transformations worksheet answers.
