Question

Complete the following sentence:Trianlge ACB is similar to __ ____________

No. Explain why they are not similar.

Answer 1

Triangle ACB is similar to Triangle DEF by SAS Similarity Theorem

see the explanation

Explanation:

we know that

The SAS Similarity Theorem, states that: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, then the triangles are similar.

In this problem

Angle B and Angle F are congruent

∠B≅∠F

The corresponding sides are

BC and FE

and

AB and DF

Verify if the ratios are proportional

`(BC)/(FE)=(AB)/(DF)`

substitute the given values

`(24)/(16)=(12)/(8)`

`1.5=1.5` -----> is true

therefore

Triangles ACB and DEF are similar by SAS Similarity Theorem