Question

ead the proof.

Given: AEEC; BDDC

Prove: △AEC ~ △BDC

Triangle A E C is shown. Line segment B D is drawn near point C to form triangle B D C.

Statement Reason
1. AEEC;BDDC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ? 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
What is the missing statement in step 4?

∠ACE ≅ ∠BCD
∠EAB ≅ ∠DBC
∠EAC ≅ ∠EAC
∠CBD ≅ ∠DBC

Answer 1

∠ACE ≅ ∠BCD

Reason: both are the same angle at C (an angle is congruent to itself — reflexive property), giving the second angle pair for AA.