Question

what is the missing step?
a. ∠2 ≅ ∠3; property of similar triangles
b. ∠2 ≅ ∠4; property of isosceles triangle
c. ab = ad; property of similar triangles
d. ec = bc; property of isosceles triangle

Explanation:

Step1: Analyze the previous steps

We know from step 5 that \(\frac{AB}{AD}=\frac{EC}{DC}\), and from step 8 that \(\frac{AB}{AD}=\frac{BC}{DC}\). By the substitution property of equality (step 8), we need to show that \(EC = BC\).

Step2: Recall the property of isosceles triangle

If a triangle has two congruent angles, then the sides opposite those angles are congruent. In \(\triangle BEC\) (implied by the given angle - side relationships in the proof), if we can establish the necessary angle - congruency (not shown in full here, but based on the flow of the proof steps), by the property of isosceles triangle (if two angles are congruent, the sides opposite are equal), \(EC = BC\) would be a valid step.

Answer:

D. \(EC = BC\); property of isosceles triangle