Fill in the missing statement and reason of the proof below in five steps and give five reasons for each, show your work.
Given: triangle, A, C, E, \cong, triangle, B, C, E, .△ACE≅△BCE.
Prove: triangle, A, C, D, \cong, triangle, B, C, D△ACD≅△BCD.
Statement: triangle ACD ≅ triangle BCD
Reasons:
1. Given: triangle ACE ≅ triangle BCE (Given)
2. AC ≅ BC (corresponding parts of congruent triangles are congruent)
3. Angle ACE ≅ Angle BCE (corresponding parts of congruent triangles are congruent)
4. CD ≅ CD (reflexive property of equality)
5. Triangle ACD ≅ Triangle BCD (Side-Angle-Side congruence theorem)
Statement: Angle A ≅ Angle B
Reasons:
1. Given: triangle ACE ≅ triangle BCE (Given)
2. Angle ACE ≅ Angle BCE (corresponding parts of congruent triangles are congruent)
3. Angle A = Angle ACE - Angle ACE = Angle BCE - Angle BCE = Angle B (Subtraction property of equality)
4. Angle A ≅ Angle B
Statement: Angle C ≅ Angle C
Reasons:
1. Reflexive property of equality
Statement: Angle D ≅ Angle D
Reasons:
1. Reflexive property of equality
Statement: AD ≅ BD
Reasons:
1. Given: triangle ACE ≅ triangle BCE (Given)
2. AC ≅ BC (corresponding parts of congruent triangles are congruent)
3. AD = AC - CD
BD = BC - CD
(Subtraction property of equality)
4. AC = BC (Given)
5. AD = BD (Substitution property of equality)