In triangle CDE, the bisector is drawn at an angle C of 90 degrees, an angle D of 30 degrees. Compare cut CF and DF.

Given:
triangle CDE;
angle C = 90 degrees,
angle D = 30 degrees.
Compare segments CF and DF.
Decision:
1) Consider triangle CDF. Since СF is a bisector, the angle DСF = 90: 2;
angle DСF = 45 degrees;
2) The sum of the degree measures of the angles of any triangle is 180 degrees.
Therefore the angle DFC = 180 – angle DСF – angle D;
angle DFC = 180 – 45 – 30;
angle DFC = 105 degrees;
3) Opposite the larger side is the larger angle, opposite the smaller side is the smaller angle.
Therefore, opposite the angle DСF = 45 degrees lies the DF side, and opposite the CF side there is an angle of 30 degrees. Then DF is greater than CF.