(03.05 mc)

prove that δabc and δedc are similar.

a. 15 over 4 equals 12 over 5 equals 9 over 3 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sas similarity postulate.
b. ∠dce is congruent to ∠bca by the vertical angles theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sas similarity postulate.
c. ∠e and ∠a are right angles; therefore, these angles are congruent since all right angles are congruent. 12 over 4 equals 9 over 3 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sss similarity postulate.
d. ∠dce is congruent to ∠cba by the vertical angles theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sss similarity postulate.