read the proof. given: ae ⊥ ec; bd ⊥ dc prove: △aec ~ △bdc what is the missing statement in step 4? ∠ace ≅…
read the proof. given: ae ⊥ ec; bd ⊥ dc prove: △aec ~ △bdc what is the missing statement in step 4? ∠ace ≅ ∠bcd ∠eab ≅ ∠dbc ∠eac ≅ ∠eac ∠cbd ≅ ∠dbc
Answer
Explanation:
Step1: Recall the AA similarity theorem
The AA (angle - angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. We already have one pair of congruent angles ($\angle AEC\cong\angle BDC$ as they are right - angles). We need to find another pair of congruent angles using the reflexive property.
Step2: Identify the common angle
The common angle between $\triangle AEC$ and $\triangle BDC$ is $\angle ACE$ and $\angle BCD$. They are the same angle, and by the reflexive property, $\angle ACE\cong\angle BCD$.
Answer:
$\angle ACE\cong\angle BCD$