Question

if a character in a video game is scaled up by a factor of 3, what happens to the corresponding sides of the triangles in the model?
a. they triple in length
b. they double in length
c. they halve in length
d. they stay the same

if two triangles have corresponding sides in the ratio 1:2, are the triangles similar?
a. yes
b. only if the angles are equal
c. no
d. none of the answers

which of the following ratios would not indicate sss similarity?
a. $\frac{2}{4},\frac{3}{6},\frac{5}{10}$
b. $\frac{1}{3},\frac{2}{6},\frac{3}{9}$
c. $\frac{4}{5},\frac{6}{7},\frac{8}{9}$
d. $\frac{5}{10},\frac{7}{14},\frac{9}{18}$

Explanation:

Step1: Understand scaling concept

When an object is scaled up by a factor of $n$, all its linear - dimensions (like side - lengths of triangles) are multiplied by $n$. Here $n = 3$, so the side - lengths of the triangles in the model triple.

Step2: Recall similarity criterion for triangles

The Side - Side - Side (SSS) similarity criterion states that if the ratios of the corresponding sides of two triangles are equal, the triangles are similar. If the ratios of corresponding sides of two triangles are in the ratio $1:2$, by the SSS similarity criterion, the triangles are similar.

Step3: Check SSS similarity ratios

For SSS similarity, the ratios of corresponding sides of two triangles must be equal.

• For option a: $\frac{2}{4}=\frac{3}{6}=\frac{5}{10}=\frac{1}{2}$
• For option b: $\frac{1}{3}=\frac{2}{6}=\frac{3}{9}=\frac{1}{3}$
• For option c: $\frac{4}{5}

eq\frac{6}{7}
eq\frac{8}{9}$

• For option d: $\frac{5}{10}=\frac{7}{14}=\frac{9}{18}=\frac{1}{2}$

Answer:

1. a. They triple in length
2. a. Yes
3. c. $\frac{4}{5},\frac{6}{7},\frac{8}{9}$