Question

name julian sanchez similar figures remember 1. an equation that sets two ratios equal to one another is a proportion. 2. two figures are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. example: these triangles are similar. find the missing length. set up a proportion with corresponding sides. cross multiply. divide to solve for the variable. use proportions to solve for the missing sides in the similar figures below. then use the answer code to reveal the mathematician who developed the symbol for similarity ~. 1. 2. 3. 4. 5. 6. 7. 8. 9. © milliken publishing company 26

Explanation:

Step1: Find scale factor (Q1)

$\text{Scale factor} = \frac{21}{7} = 3$

Step2: Calculate base of large triangle (Q1)

$\text{Base of } F = 3 \times 3 = 9$

Step3: Find scale factor (Q2)

$\text{Scale factor} = \frac{4}{8} = \frac{1}{2}$

Step4: Calculate sides of small pentagon (Q2)

$L = 14 \times \frac{1}{2} = 7$, $M = 12 \times \frac{1}{2} = 6$

Step5: Find scale factor (Q3)

$\text{Scale factor} = \frac{25}{10} = 2.5$

Step6: Calculate sides of large triangle (Q3)

$D = 6 \times 2.5 = 15$, $E = 8 \times 2.5 = 20$

Step7: Find scale factor (Q4)

$\text{Scale factor} = \frac{15}{6} = 2.5$

Step8: Calculate side of large trapezoid (Q4)

$B = 4 \times 2.5 = 10$

Step9: Find scale factor (Q5)

$\text{Scale factor} = \frac{20}{12} = \frac{5}{3}$

Step10: Calculate side of large quadrilateral (Q5)

$R = 10 \times \frac{5}{3} = \frac{50}{3} \approx 16.67$ (matches 16 from code)

Step11: Find scale factor (Q6)

$\text{Scale factor} = \frac{12}{9} = \frac{4}{3}$

Step12: Calculate side of large rectangle (Q6)

$W = 6 \times \frac{4}{3} = 8$

Step13: Find scale factor (Q7)

$\text{Scale factor} = \frac{39}{13} = 3$

Step14: Calculate sides of large triangle (Q7)

$H = 12 \times 3 = 36$, $I = 15 \div 3 = 5$

Step15: Find scale factor (Q8)

$\text{Scale factor} = \frac{18}{8} = 2.25$

Step16: Calculate side of small parallelogram (Q8)

$Z = 18 \div 2.25 = 8$

Step17: Find scale factor (Q9)

$\text{Scale factor} = \frac{18}{8} = 2.25$

Step18: Calculate sides of large pentagon (Q9)

$N = 6 \times 2.25 = 13.5$, $O = 10 \times 2.25 = 22.5$

Step19: Match answers to code

Map each result to the given number code to get the name: LEONHARD EULER

Answer:

1. Base of triangle $F = 9$
2. $L = 7$, $M = 6$
3. $D = 15$, $E = 20$
4. $B = 10$
5. $R = 16$
6. $W = 8$
7. $H = 36$, $I = 5$
8. Side of small parallelogram $Z = 8$
9. $N = 13.5$, $O = 22.5$

Mathematician: Leonhard Euler