Question

100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!

Answer 1

`(4)/(3)`

Explanation:

In similar triangles, corresponding angles are the same size. Therefore, if triangle ABC is similar to triangle DEF then:

• ∠A ≅ ∠D
• ∠B ≅ ∠E
• ∠C ≅ ∠F

The standard convention is to label the sides of a triangle with lowercase letters that correspond to the vertices they are opposite to.

In similar triangles, corresponding sides are always in the same ratio. Therefore:

• a : d = b : e = c : f

If similar triangles ABC and DEF have a scale ratio of 1/3, it means that each side of triangle ABC is 1/3 the length of the corresponding side in triangle DEF. Therefore, as side d is the corresponding side to side a:

`\begin{aligned}\textsf{Length of $a$} &= \textsf{Scale ratio}* \textsf{Length of $d$} \\\\&=(1)/(3) * 4\\\\&=(4)/(3)\end{aligned}`

So, the length of side d is 4/3 units.

Answer 2

If the scale ratio of two similar triangles is 1/3, that means the corresponding sides of the two triangles are in the same ratio.

If side 'd' of triangle DEF has a length of 4, and the scale ratio of the two triangles is 1/3, then the length of the corresponding side 'a' of triangle ABC can be found as follows:

a/d = 1/3

a = (1/3)d

a = (1/3)4

a = 4/3

Therefore, the length of side 'a' is 4/3.