Question

How is triangle FGE similar to triangle CDE, find DE

Answer 1

Triangles FGE and CDE are similar if their corresponding angles are congruent and their corresponding sides are in proportion Therefore, DE=56.

Triangles FGE and CDE are similar if their corresponding angles are congruent and their corresponding sides are in proportion.

Given that

CE=3x+2, EF=10, DE=5x+1, and EG=16, we can set up a proportion to find DE.

In similar triangles, the ratios of corresponding sides are equal:

`(CE)/(DE) = (EF)/(EG)`

Substituting the given values:

`(3x+2)/(5x+1) = (10)/(16)`

Now, solve for x:

`(3x+2)/(5x+1) = (10)/(16)`

16(3x+2)=10(5x+1)

48x+32=50x+10

32−10=50x−48x

22=2x

x=
`(22)/(2)`

x=11

Now that we have found x=11, let's substitute it back in

DE=5x+1:

DE=5x+1

DE=5(11)+1

DE=55+1

DE=56

Therefore, DE=56.

Answer 2

They are similar because of the AAA similarity test

Since E is an opposite angle by the vertex then the angles are equal, and angle C and G are equal because they are alternate interior angles, similarly D and F are equal because they are alternate interior angles.

Then

(3x+2) /16 = (5x+1)/10

solving the equation x=0.08

and DE would be 1.4