Question

similar figures examples
find the scale factor for the images
a.
b.
write the similarity statements & find the scale factor.
a.
b
find the value of the variables
a
b. given cdef ~ ghij,
c. given efgh ~ ijkl.
d. given δhgq ~ δtpf

Explanation:

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Part 1: Find the scale factor for the images

a. Dog figures

Step1: Identify corresponding sides

Original height = 5, Enlarged height = 15

Step2: Calculate scale factor

$\text{Scale Factor} = \frac{\text{Enlarged}}{\text{Original}} = \frac{15}{5} = 3$

b. Letter C figures

Step1: Identify corresponding sides

Original height = 8, Enlarged height = 24

Step2: Calculate scale factor

$\text{Scale Factor} = \frac{\text{Enlarged}}{\text{Original}} = \frac{24}{8} = 3$

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Part 2: Similarity statements & scale factor

a. Quadrilaterals

Step1: Write similarity statement

$ABCD \sim EFGH$

Step2: Calculate scale factor

$\text{Scale Factor} = \frac{10}{5} = 2$

b. Triangles

Step1: Write similarity statement

$\triangle ABC \sim \triangle DFE$

Step2: Calculate scale factor

$\text{Scale Factor} = \frac{6}{3} = 2$

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Part 3: Find the value of the variables

a. Similar triangles $\triangle ABC \sim \triangle DEF$

Step1: Find scale factor

$\text{Scale Factor} = \frac{12}{15} = \frac{4}{5}$

Step2: Solve for $x$

$x = 25 \times \frac{4}{5} = 20$

Step3: Solve for $y$

$y = 12 \times \frac{4}{5} = 9.6$

b. Similar quadrilaterals $CDEF \sim GHIJ$

Step1: Find scale factor

$\text{Scale Factor} = \frac{28}{7} = 4$

Step2: Solve for $x$

$x = 22 \times 4 = 88$

Step3: Solve for $z$

$z = 5 \times 4 = 20$

c. Similar quadrilaterals $EFGH \sim IJKL$

Step1: Find scale factor

$\text{Scale Factor} = \frac{100}{27}$

Step2: Solve for $x$

$x = 11 \times \frac{100}{27} \approx 40.74$

Step3: Solve for $y$

$y = 66 \times \frac{27}{100} = 17.82$

Step4: Solve for $m$

$m = 110^\circ$ (corresponding angles of similar figures are equal)

d. Similar triangles $\triangle HGQ \sim \triangle TPF$

Step1: Find scale factor

$\text{Scale Factor} = \frac{20}{10} = 2$

Step2: Solve for $y$

$y = 4 \times 2 = 8$

Step3: Solve for $z$

$z = 10 \times 2 = 20$

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Answer:

Part 1:

a. 3
b. 3

Part 2:

a. Similarity statement: $ABCD \sim EFGH$; Scale factor: 2
b. Similarity statement: $\triangle ABC \sim \triangle DFE$; Scale factor: 2

Part 3:

a. $x=20$, $y=9.6$
b. $x=88$, $z=20$
c. $x\approx40.74$, $y=17.82$, $m=110^\circ$
d. $y=8$, $z=20$