Similar Triangles with 24° Angles: Comparing ABC and DEF

Question

Look at the triangles in the diagram.

Which of the following statements is true?

242424242424444666666444AAACCCBBBEEEFFFDDD

Step-by-Step Solution

This question actually has two steps:

In the first step, you must define if the triangles are congruent or not,

and then identify the correct answer among the options.

 

Let's look at the triangles: we have two equal sides and one angle,

But this is not a common angle, therefore, it cannot be proven according to the S.A.S theorem

Remember the fourth congruence theorem - S.A.A
If the two triangles are equal to each other in terms of the lengths of the two sides and the angle opposite to the side that is the largest, then the triangles are congruent.

 

But the angle we have is not opposite to the larger side, but to the smaller side,

Therefore, it is not possible to prove that the triangles are congruent and no theorem can be established.

Answer

It is not possible to calculate.