Question

Which of the following is an accurate similarity statement for the pictured triangles?

A. ΔABD ~ ΔBCD
B. ΔABD ~ ΔACB
C. ΔACB ~ ΔBCD
D. All of these are accurate similarity statements.

Answer 1

@JakeV8

Answer 2

@AriPotta

Answer 3

@ajprincess

Answer 4

please help

Answer 5

i think it's d

Answer 6

@alainabbyboo22 I'm sorry, I had to log off earlier... I agree with AriPotta, I think it's D.

One important thing is to match up the similar parts of the two triangles you are comparing... like ABD starts with segment AB which is the hypotenuse of triangle ABD... similarly, triangle BCD starts with segment BC which is its hypotenuse.

However, the really important thing is that there is a common side in BD. All the geometry theorems require you to know something like that to relate 2 triangles... you can't just say 2 right triangles are similar because they both have a hypotenuse... this is sort of an obvious point if you sketch out 2 very very different right triangles, say an isosceles right triangle compared to a right triangle with one leg super long and one leg super short.

In this problem, you did have that common side which allows the various theorems to work, so all is well in the Land of Similar Triangles. :)