Angles DCE and DEC have equal measure,
Angles AEB and ABE have equal measure.
1. mDCE = mDEC 1. Given
2. mDEC = mAEB 2. Vertical Angles Theorem
3. mDCE = mAEB 3. Transitive Property of Equality
4. mAEB = mABE 4. Given
5. mDCE = mABE 5. Transitive Property of Equality
Proofs like these prepare students for proofs later on in the text. Notice that the two isosceles triangles DCE and ABE are in fact similar -- and indeed congruent if we were given another statement such as "E is the midpoint of