Question

Read the proof.

Answer 1

Solution:

Given: In ΔA EC and Δ B DC  

Prove: Δ A EC ~ ΔB DC

Proof:

1. In Δ A EC and ΔB DC

2. ∠A EC = ∠B DC= 90°→→definition of perpendicular

3. ∠A EC ≅ ∠B DC →→All right angles are congruent

4. ∠ACE=∠BCD=∠ACE→→Reflexive property

5. ΔAEC ~ ΔBDC→→→AA similarity theorem

Option A : .∠ACE ≅ ∠ACE is true.

Answer 2

The reflexive property of equality states that a value is equal to itself. (i.e. for all real numbers, x = x.)

Given that the reason for the missing statement, it means that the similarlity statement is equal to it self.

Having proved in statement 3 that ∠AEC ≅ ∠BDC both being right angles, it can be seen that the angle both have in common is angle C.

Thus, to statement 4 shows that angle C is congrent to itself.

Therefore, the missing statement in step 4 is ∠ACE ≅ ∠ACE