Question

There are two triangles. For the first triangle, the vertices are A, B and C. m<A =65
degrees, m<B=70 degrees and BC = 8. The second triangle has the vertices
E, F and D. m<F = 65 degrees and m<D = 45 degrees. DE = 8. Are the two
triangles congruent and if yes, how do you know? Which segment is congruent to AB

Answer 1

To determine if the two triangles are congruent, we need to compare their corresponding sides and angles.

For the first triangle (ABC), we are given that angle A measures 65 degrees and angle B measures 70 degrees. We don't have any information about angle C. We also know that side BC measures 8 units.

For the second triangle (EFD), we are given that angle F measures 65 degrees and angle D measures 45 degrees. We don't have any information about angle E. We also know that side DE measures 8 units.

Looking at the angles, we have angle A in triangle ABC and angle D in triangle EFD. These angles are different, so the triangles are not congruent based on angle-angle (AA) similarity.

Next, let's compare the sides. We have side BC in triangle ABC and side DE in triangle EFD. These sides are congruent because they both measure 8 units.

So, the segment congruent to AB is DE, which measures 8 units.