Congruence of ACB & CED: Similarity Chapter

[slwarrior64]

Only use that ACB and CED are congruent, not any other symbols in the diagram.

 

[HOI]

I don't think "similarity" is useful here (and the two triangles are definitely NOT "congruent". We are given that triangle ABC is a right triangle. (It is not specifically said that triangle CED is a right triangle but if angle CDE is not a right angle this problem is un-doable.) Angle ACB is congruent to angle CED. Since both triangles are right angles it follows that angles CAB and DCE are congruent and then that angle ACE is a right angle! So triangle ACE is a right triangle with legs of length 7 and 24. The length of AE follows from the Pythagorean theorem.