Is there enough information to prove triangles congruent, if so write congruence statment and state method used, eg angle side angle theorem

Question

Answer 1

So the goal here is to consider the methods used to prove congruence (Side Side Side, Side Angle Side, or Angle Side Angle) and work from there. Another trick for this particular problem set is to notice when two triangles that might be congruent share a side in common!

Keep reading for solutions:

9) We know that the triangles already share two sides with the same length: AD = BC = 13, and AB = CD = 16. The trick here is that the two shapes share a side in common (BD). Therefore, by side side side, they are congruent.

10) This relies on knowing that line KM is perpendicular to line LJ. Since that’s the case, both KLJ and MLJ are right angles. This means that angles KJL and LKJ are complementary, since they’re two angles in a right triangle. Since 90-58=32, this means that angle KJL (32 degrees) is the same as angle MJL. Since triangles KLJ and MLJ share a common side (JL) and KLJ and MLJ are both right angles, the two triangles are congruent by Angle Side Angle.

11) Trick question: You know that the angles are the same in both triangles, but is there an angle angle angle congruence theorem? There isn’t—all this does is prove similarity, not congruence. You need at least one corresponding side to be congruent for the two triangles to be congruent.

12) You already know angle HEG = angle FEH, and that angle FGE= angle HE. Since they share a side (EG), triangles HEG and FEG are congruent by angle side angle.