Question

Can the triangles below be proven similar?

Answer 1

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Yes ! they ofcourse are similar and here goes the explanation behind that ~

two triangles are said to be similar by SAS postulate in case the ratios of their side lengths comes out to be equal along with one angle lying in between the side lengths

in this case ,

$\frac{AB}{BD} \: should \: be \: equal \: to \: \frac{EB}{BC}$

so , let's check if the ratio is equal or no ~

$\implies\frac{AB}{BD} = \frac{27}{18} = \frac{3}{2} \\ \\ \implies \: \frac{EB}{BC} = \frac{36}{24} = \frac{3}{2} \\ \\ \therefore \: \frac{AB}{BD} = \frac{EB}{BC}$

Also ,

∠ABE = ∠CBD

since they both are vertically opposite , i.e. , angles with the same vertex B .

thus the triangles are similar by SAS postulate !

hence , Option A is correct !

hope helpful ~