Below are photos of a ragwing C-170 (no dorsal) and C-170A (with dorsal). Former Cessna engineer and test pilot William Thompson wrote (
Cessna - Wings for the World: The Single-Engine Development Story, p. 25):
The dorsal fin, borrowed from the C-195, was added to the C-170A to prevent abnormally large angles of yaw with full rudder deflection in flight. [...] In addition, an optional floatplane version was planned, and that would be even more critical in directional stability. To pass the test after release of full rudder pedal travel, the airplane would have to return to close to the original heading. The addition of the dorsal fin would not be noticeable to the pilot except for a slight deterioration in rudder control during taxi operations.
Dorsal fins were carried over into the C-172. The larger dorsal fin on the 1972 C-172L finally eliminated the elusive "pitch-down" phenomenon sometimes encountered in full-flap slips.
Dorsal fins can also look "cool" and are sometimes added for purely cosmetic reasons -- the 1972 and later PA-28 and PA-32 series, for example.
What is a "Strake",
bonus points if you don't google
red star if you provide a pic
Example on the Cessna Model 318 (T-37) -- in flight test, the tadpole-shaped forward fuselage created unwanted lift that impaired spin recovery, so strakes (third photo, circled in yellow) were added to modify the airflow. IIRC, the aerobatic Beech Musketeers also had strakes. Grumman American tested strakes and ventral fin on its AA-1B for a planned "spin package", as well.