Question

each pair of figures is similar. find the missing side. 1) 2) 3) 4) 5) 6) 7) 8)

Explanation:

1. For the first pair of similar triangles (problem 1):

• Explanation:
• Step 1: Find the scale - factor
• The scale - factor is found by comparing corresponding sides. For the non - base sides, if we take the ratio of the sides of the larger triangle to the smaller triangle, $\frac{16}{8}=2$.
• Let the missing base be $x$. Since the figures are similar, the ratios of corresponding sides are equal. So, $\frac{10}{x}=2$.
• Step 2: Solve for the missing side
• Cross - multiply to get $10 = 2x$. Then, $x=\frac{10}{2}=5$.

1. For the second pair of similar right - triangles (problem 2):

• Explanation:
• Step 1: Find the scale - factor
• Compare the hypotenuses: $\frac{30}{15}=2$. Let the missing side be $y$.
• Since the triangles are similar, $\frac{y}{9}=2$.
• Step 2: Solve for the missing side
• Multiply both sides by 9 to get $y = 18$.

1. For the third pair of similar triangles (problem 3):

• Explanation:
• Step 1: Find the scale - factor
• The scale - factor from the larger triangle to the smaller triangle for the non - base sides is $\frac{16}{4}=4$.
• Let the missing base be $z$. Then, $\frac{12}{z}=4$.
• Step 2: Solve for the missing side
• Cross - multiply: $12 = 4z$, so $z=\frac{12}{4}=3$.

1. For the fourth pair of similar right - triangles (problem 4):

• Explanation:
• Step 1: Find the scale - factor
• Compare the hypotenuses: $\frac{40}{20}=2$. Let the missing side be $a$.
• Since the triangles are similar, $\frac{a}{12}=2$.
• Step 2: Solve for the missing side
• Multiply both sides by 12 to get $a = 24$.

1. For the fifth pair of similar trapezoids (problem 5):

• Explanation:
• Step 1: Find the scale - factor
• Compare the non - parallel sides: $\frac{36}{4}=9$. Let the missing parallel side be $b$.
• Then, $\frac{81}{b}=9$.
• Step 2: Solve for the missing side
• Cross - multiply: $81 = 9b$, so $b=\frac{81}{9}=9$.

1. For the sixth pair of similar trapezoids (problem 6):

• Explanation:
• Step 1: Find the scale - factor
• Compare the non - parallel sides: $\frac{25}{5}=5$. Let the missing parallel side be $c$.
• Then, $\frac{40}{c}=5$.
• Step 2: Solve for the missing side
• Cross - multiply: $40 = 5c$, so $c=\frac{40}{5}=8$.

1. For the seventh pair of similar triangles (problem 7):

• Explanation:
• Step 1: Find the scale - factor
• Compare the non - base sides: $\frac{40}{8}=5$. Let the missing base be $d$.
• Then, $\frac{60}{d}=5$.
• Step 2: Solve for the missing side
• Cross - multiply: $60 = 5d$, so $d=\frac{60}{5}=12$.

1. For the eighth pair of similar triangles (problem 8):

• Explanation:
• Step 1: Find the scale - factor
• Compare the non - base sides: $\frac{18}{9}=2$. Let the missing base be $e$.
• Then, $\frac{32}{e}=2$.
• Step 2: Solve for the missing side
• Cross - multiply: $32 = 2e$, so $e=\frac{32}{2}=16$.

Answer:

1. 5
2. 18
3. 3
4. 24
5. 9
6. 8
7. 12
8. 16