1. BE || CD 1. Given
2. ∠A ≅ ∠A 2. Reflexive Property
3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅.
∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅.
5. ΔABE ∼ ΔACD 5. AA Similarity Postulate
6.
AC
AB
=
AD
AE
6. Definition of Similar Triangles
7. AC = AB + BC, AD = AE + ED 7. Segment Addition Postulate
8.
AB + BC
AB
=
AE + ED
AE
8. Substitution
9.
AB
AB
+
BC
AB
=
AE
AE
+
ED
AE
9. Addition
10.
BC
AB
=
ED
AE
10. ???
Fill in the missing reason for the proof.
A) Transitive Property
B) Subtraction Property
C) SSS Similarity Theorem
D) Segment Addition Postulate