Question

1. which of the following ratios would not indicate sss similarity?

a. 1/2, 3/6, 4/8
b. 1/3, 2/6, 1/6
c. 3/10, 7/12, 8/18
d. 3/4, 3/4, 8/12

1. which of the following triangles would not be similar by sss?

a. triangles with sides 5, 12, 13 and 10, 24, 26
b. triangles with sides 3, 4, 5 and 6, 8, 10
c. triangles with sides 2, 3, 4 and 4, 6, 9
d. triangles with sides 7, 24, 25 and 14, 48, 50

1. what happens to the perimeter of a triangle when it is scaled by a factor of 3?

a. it doubles
b. it remains the same
c. it triples
d. it quadruples

Explanation:

Step1: Recall SSS - similarity criterion

Two triangles are similar by SSS (Side - Side - Side) if the ratios of their corresponding sides are equal.

Step2: Analyze question 4

For option a: $\frac{1}{2},\frac{2}{4},\frac{3}{6}=\frac{1}{2},\frac{1}{2},\frac{1}{2}$ (equal ratios, indicates SSS similarity).
For option b: $\frac{3}{6},\frac{2}{4},\frac{1}{2}=\frac{1}{2},\frac{1}{2},\frac{1}{2}$ (equal ratios, indicates SSS similarity).
For option c: $\frac{3}{10},\frac{7}{12},\frac{8}{11}$ (unequal ratios, does not indicate SSS similarity).
For option d: $\frac{3}{6},\frac{3}{6},\frac{6}{12}=\frac{1}{2},\frac{1}{2},\frac{1}{2}$ (equal ratios, indicates SSS similarity).

Step3: Analyze question 5

For option a: $\frac{5}{10}=\frac{12}{24}=\frac{13}{26}=\frac{1}{2}$, triangles are similar by SSS.
For option b: $\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}$, triangles are similar by SSS.
For option c: $\frac{2}{4}=\frac{3}{6}
eq\frac{4}{9}$, triangles are not similar by SSS.
For option d: $\frac{7}{14}=\frac{24}{48}=\frac{25}{50}=\frac{1}{2}$, triangles are similar by SSS.

Step4: Analyze question 6

Let the sides of the original triangle be $a$, $b$, and $c$, so the perimeter $P = a + b + c$. When scaled by a factor of 3, the new sides are $3a$, $3b$, and $3c$, and the new perimeter $P'=3a + 3b+3c = 3(a + b + c)=3P$. So the perimeter triples.

Answer:

1. C. $\frac{3}{10},\frac{7}{12},\frac{8}{11}$
2. C. Triangles with sides 2, 3, 4 and 4, 6, 9
3. C. It triples