Question

NEED HELP ASAP 30 points

Is △DBE similar to △ABC ? If so, which postulate or theorem proves these two triangles are similar?




​ △DBE ​ is similar to ​ △ABC ​ by the ​ SAS Similarity Theorem ​.

​ △DBE ​ is similar to ​ △ABC ​ by the ​ SSA Similarity Theorem ​.

​ △DBE ​ is similar to ​ △ABC ​ by the ​ SSS Similarity Theorem ​.

​ △DBE ​ is not similar to ​ △ABC ​.

Answer 1

△DBE ​ is similar to ​ △ABC ​ by the ​ SAS Similarity Theorem ​.

Given triangles in figure

Explanation:

we have to tell that is the triangles are similar or if similar then by which postulate.

In ΔDBE and ΔABC,

⇒

⇒

Hence, the sides of triangle are proportional.

And also ∠B=∠B (common) i.e the one angle congruent

Hence, △DBE ​ is similar to ​ △ABC ​ by the ​ SAS Similarity Theorem ​.

Answer 2

△DBE ​ is similar to ​ △ABC ​ by the ​ SAS Similarity Theorem ​.

Explanation:

Given triangles in figure

we have to tell that is the triangles are similar or if similar then by which postulate.

In ΔDBE and ΔABC,

`(DB)/(AB) =(EB)/(CB)`

⇒
`(10)/(10+15)= (16)/(16+40)`

⇒
`(2)/(5)=(2)/(5)`

Hence, the sides of triangle are proportional.

And also ∠B=∠B (common) i.e the one angle congruent

Hence, △DBE ​ is similar to ​ △ABC ​ by the ​ SAS Similarity Theorem ​.