Question

The sides of two triangles are 6, 9, 12 inches and 2.5, 3.75, and 5 inches respectively. Are the triangles similar ? Explain your reasoning.

Answer 1

Yes, the triangles are similar because the ratio of the length of corresponding sides are equal

Explanation:

If the two figures have same shape, they are called similar.

When two figure are similar , then the ratio of the length of their corresponding sides are equal.

Given: the sides of two triangles are 6, 9, 12 inches and 2.5, 3.75 and 5 inches.

then;

`(6)/(2.5) =2.4`

`(9)/(3.75) =2.4`

`(12)/(5) =2.4`

⇒
`(6)/(9)=(9)/(3.75)=(12)/(5)`

by definition of similar, we have;

the given triangles are similar.

Answer 2

Triangles must be similar

Explanation:

We are given two triangles

First triangle:

sides are 6 , 9 , 12

Second triangle:

2.5, 3.75 , 5

We know that if two triangles are similar , then their ratio of sides must be equal

so, we will find ratio of side of each corresponding sides

and then we check whether they are equal

we get

`(6)/(2.5)=(9)/(3.75)=(12)/(5)`

now, we can find each ratios and check whether they are equal

`2.4=2.4=2.4`

we can see that

all values are equal and same

so, the ratio of their sides are equal

Hence , triangles must be similar