The bisector EF is drawn in triangle CDE. Angle C = 90 *, Angle D = 30 *. Prove that triangle

The bisector EF is drawn in triangle CDE. Angle C = 90 *, Angle D = 30 *. Prove that triangle DEF is isosceles. Compare segments CF and DF

Find the unknown angle E in the right-angled triangle CDE:
Angle E = 90 ° – angle D = 90 ° – 30 ° = 60 °.
Consider a triangle DFE, in which the angle D = 30 ° (by condition), the angle E = 30 ° (EF is the bisector of the angle DEC). We get that the DFE triangle is isosceles (two angles are equal). Q.E.D.

Now consider the triangle FCE, in which the leg CF lies opposite the angle of 30 ° and this means that it is equal to half of the hypotenuse EF. In turn, EF = DF (sides of an isosceles triangle). We can conclude that СF is two times less than DF.