Corresponding Angles Of Similar Of Triangles Independent Practice ... - Free Printable

Problem Analysis:

The worksheet involves solving problems related to similar triangles. The key concept here is that corresponding sides of similar triangles are proportional. We will solve each problem step by step.

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Problem 1: Find \( h \)

#### Given:
- Two triangles are similar.
- The larger triangle has a base of 7.5 m and a height of 8 m.
- The smaller triangle has a base of 2.5 m and an unknown height \( h \).

#### Solution:
Since the triangles are similar, the ratios of their corresponding sides are equal. Therefore:
\[
\frac{\text{Height of smaller triangle}}{\text{Height of larger triangle}} = \frac{\text{Base of smaller triangle}}{\text{Base of larger triangle}}
\]
Substitute the given values:
\[
\frac{h}{8} = \frac{2.5}{7.5}
\]
Simplify the ratio on the right-hand side:
\[
\frac{2.5}{7.5} = \frac{1}{3}
\]
So the equation becomes:
\[
\frac{h}{8} = \frac{1}{3}
\]
To solve for \( h \), cross-multiply:
\[
h \cdot 3 = 8 \cdot 1
\]
\[
3h = 8
\]
\[
h = \frac{8}{3}
\]
\[
h = 2.67 \, \text{m (approximately)}
\]

#### Final Answer for Problem 1:
\[
\boxed{2.67}
\]

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Problem 2: Find \( m \)

#### Given:
- Triangles \( \triangle ABC \) and \( \triangle DEF \) are similar.
- In \( \triangle ABC \):
- \( AB = 3 \, \text{yd} \)
- \( BC = 4 \, \text{yd} \)
- \( AC = 5 \, \text{yd} \) (hypotenuse)
- In \( \triangle DEF \):
- \( DE = 7 \, \text{yd} \)
- \( EF = m \, \text{yd} \)
- \( DF = 9 \, \text{yd} \)

#### Solution:
Since the triangles are similar, the ratios of their corresponding sides are equal. We can use the ratio of the hypotenuses to find \( m \):
\[
\frac{\text{Hypotenuse of } \triangle DEF}{\text{Hypotenuse of } \triangle ABC} = \frac{\text{Side } EF}{\text{Side } BC}
\]
Substitute the known values:
\[
\frac{9}{5} = \frac{m}{4}
\]
Cross-multiply to solve for \( m \):
\[
9 \cdot 4 = 5 \cdot m
\]
\[
36 = 5m
\]
\[
m = \frac{36}{5}
\]
\[
m = 7.2 \, \text{yd}
\]

#### Final Answer for Problem 2:
\[
\boxed{7.2}
\]

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Problem 3: Find \( m \)

#### Given:
- Two triangles are similar.
- In the smaller triangle:
- One leg is 3.3 m.
- The other leg is 1 m.
- In the larger triangle:
- One leg is 7 m.
- The other leg is \( m \) m.

#### Solution:
Since the triangles are similar, the ratios of their corresponding sides are equal. We can use the ratio of the known legs to find \( m \):
\[
\frac{\text{Leg of larger triangle}}{\text{Leg of smaller triangle}} = \frac{\text{Other leg of larger triangle}}{\text{Other leg of smaller triangle}}
\]
Substitute the known values:
\[
\frac{7}{3.3} = \frac{m}{1}
\]
This simplifies to:
\[
\frac{7}{3.3} = m
\]
Calculate the value:
\[
m = \frac{7}{3.3} \approx 2.12 \, \text{m}
\]

#### Final Answer for Problem 3:
\[
\boxed{2.12}
\]

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Final Answers:

1. \( \boxed{2.67} \)
2. \( \boxed{7.2} \)
3. \( \boxed{2.12} \)