Question

1. (overline{de}paralleloverline{ac}) given
2. (angle cabcongangle edb)(angle acbcongangle deb) if two parallel lines are cut by a transversal, the corresponding angles are congruent.
3. (\triangle abcsim\triangle dbe) aa criterion for similarity
4. corresponding sides of similar triangles are proportional.
5. (ab = ad + db)(cb = ce + eb) segment addition
6. (\frac{ad + db}{db}=\frac{ce + eb}{eb}) substitution property of equality
7. (\frac{ad}{db}+1=\frac{ce}{eb}+1) division
8. (\frac{ad}{db}=\frac{ce}{eb}) subtraction property of equality

what is the missing statement in the proof? scroll down to see the entire proof.
(\bigcirc) a. (\frac{ab}{db}=\frac{cb}{eb})
(\bigcirc) b. (\frac{ab}{cb}=\frac{db}{eb})
(\bigcirc) c. (\frac{ab}{db}=\frac{cb}{eb})
(\bigcirc) d. (\frac{ab}{cb}=\frac{ac}{db})

Explanation:

Step1: Analyze the properties of similar triangles

Since \(\triangle ABC\sim\triangle DBE\) (by AA criterion for similarity), for similar triangles, the ratio of corresponding sides is equal. That is, \(\frac{AB}{DB}=\frac{CB}{EB}\)

Answer:

C. \(\frac{AB}{DB}=\frac{CB}{EB}\)