Question

Given that ∠ABD is similar to ∠ACE, what is the value of X? Round your answer to the nearest tenth

Answer 1

Do you mean Angle ABD is congruent to Angle ACE? Because we don't talk about angles being similar.

Answer 2

yes

Answer 3

So what does that mean about BD and CE?

Answer 4

they are congruent

Answer 5

Well no ... I mean one is clearly longer than the other so they can't be congruent. but Look at what angles are congruent... When two angles like that are congruent what does that mean about the two line segments.

Answer 6

are they equal?

Answer 7

No the line segments are not equal...Congruent corresponding angles make the adjacent line segments PARALLEL...Gotta remember about parallelism it goes up often in math, SAT and ACT stuff

Answer 8

But anyway what does this mean about the triangle ACE and triangle ABD?

Answer 9

Assuming BD||CE..........

Answer 10

1)We can prove the two triangles are similar....

Answer 11

You don't have to assume that BD is parallel to CE...it is known as a direct result from angle ACE being congruent to ACE

Answer 12

Use the formula........"corresponding" sides of two similar triangles are in the same ratio!!

Answer 13

Well it looks like @cambrige is taking over in assisting so... I will take leave.

Answer 14

so here,
(AB/AC)=(BC/BD)=(AD/AE)

Answer 15

it means that corresponding sides maintain a ratio between them
that is the any side you may pick will have a common ratio to the other
say for example we can say that, the bottom of both triangles are correspondent, thus

5.0 corresponds to 7.4 and their ratio will be 5/7.4

we can also say that the right side of the smaller one, "x", corresponds to the right side of the bigger one, x+2.7
what's their ratio? well x/(x+2.7)

or in ratio terms we can say that \(\bf \cfrac{5}{7.4}=\cfrac{x}{x+2.7}\)
then just solve for "x"

Answer 16

Using this relation @banana9715 , find out the value of x!!

Answer 17

Will dat be suffice or d'ya need more help @banana9715 ??

Answer 18

Thats good. Thank You!!!

Answer 19

mOST wELCOME!!