The bisector EF is drawn in the triangle CDE, the angle D is 30 degrees, the angle C is 90 degrees

The bisector EF is drawn in the triangle CDE, the angle D is 30 degrees, the angle C is 90 degrees a) prove that the triangle DEF is isosceles b) Compare the segments CF and DF

a) Since the triangle CDE given to us is rectangular (angle C is a straight line), and angle D is 30 °, then the angle E is 90 ° – 30 ° = 60 °. Since EF is a bisector, the angle DEF = angle CEF = 30 °. Now consider the triangle DEF. Angle DEF = 30 °, angle D = 30 °, therefore triangle DEF is isosceles.
b) Since the triangle DEF is isosceles, then DF = EF. Consider the triangle CEF. It is rectangular, angle CEF = 30 °, which means CF = EF / 2. So CF = DF / 2.