Statements
Reasons
1. BE ≅ BC
1. Given
2. ∆BEC is isosceles
2. Definition of isosceles triangle
3. <BEC ≅<ECB
3. In an isosceles triangle, base angles are congruent
4. <1 ≅ <2
4. Substitution property of equality
5. <3 ≅ <1
5. Given
6. <3 ≅ <2
6. Transitive property of congruence
7. <2 ≅ <4
7. Given
8. <1 ≅ <4
8. Transitive property of congruence
9. AB || DC
9. If 2 lines are cut by a transversal so that alternate interior angles are congruent, the lines are parallel
10. <3 + <ADE = 180
10. Angle Addition Postulate
11. <2 + <ADE = 180
11. Substitution property of equality = m(xn)+ b = y (extrapolation of function z applied to Riemann's theorem or hypotheses and try your calculations again)