The following outline lists some of the parallels, primarily liturgical, between Purim and the 9th of Av.
1 Maariv - Nighttime 1.1 Only Megillos that are read at night. 1.1.1 Eicho 1.1.2 Esther 1.2 Similar Structure with Kaddish Tiskabel and v'Ato Kodosh 2 Shacharis - Omissions 2.1 Purim - A "miracle" Holiday , no Hallel (Megillo instead) 2.2 9th of Av - A Fast Day without 2.2.1 Selichos (Kinnos instead) 2.2.2 Tachanun & Ovinu Malkeinu 3 Shacharis - Chazoros Hashatz 3.1 Only weekday repetitions of the Amido with Krovos/Krovatz 4 Preceding Shabbos 4.1 Purim preceded by Zachor 4.2 9 Av preceded by Chazon 5 Tanach Pattern - Special Torah and Haftoro readings are read the Shabbos before the event, with the corresponding Megilloh on the day of the event. 5.1 Purim - The Amalek Connection 5.1.1 Torah- Zachor 5.1.2 Navi - Haftoro of Zachor (Shaul's War with Amalek in Shmuel) 5.1.3 Kesuvim Esther 5.2 9 Av - The Eicho Connection 5.2.1 Torah - Eicho in Devorim 5.2.2 Navi - Eicho in the Haftoro of Chazon (Yeshaya) 5.2.3 Kesuvim - Eicho 6 Month-wide 6.1 Mishenichnos Adar Marbin b'Simcho 6.2 Mishenichnos Av M'maatin b'Simcho 7 Miscellaneous 7.1 Some Pesukim in Esther are read to Eicho melody (in particular Asher Heglo) 7.2 Chiyuv S'eudo vs. Chiyuv Taanis 7.3 Similar Minhogim not to work ================================
Shalom
RRW