Question

In the triangles, Line segment A C is-congruent-to line segment F E and Line segment B C is-congruent-to line segment D E.

Triangles A B C and F D E are shown. The lengths of sides A C and F E are congruent. The lengths of sides B C and D E are congruent. Angle B C A is 72 degrees. Angle D E F is 65 degrees.

Which statement correctly compares Line segment A B and Line segment F D?

Line segment A B and Line segment F D are the same length.
Line segment A B is longer than Line segment F D.
Line segment A B is shorter than Line segment F D.
Line segment A B is shorter than or the same length as Line segment F D.

Answer 1

Line segment A B is longer than Line segment F D.

Explanation:

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Answer 2

Line segment A B is longer than Line segment F D.

Explanation:

If Angle BCA angle DEF would was congruent, then the triangles would be congruent too, because they would satisfied the Side Angle Side (SAS) postulate. Therefore, line segment A B and line segment F D are not the same length.

Given that angle BCA is bigger than angle DEF, and the congruency between sides, then, line segment A B is longer than line segment F D.