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
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.