Here's a Two Column Proof:
Statement Reason
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1. Triangle ABC is isosceles Given
2. Angle DAC = Angle DBC Definition of Isosceles
3. Segment CD = Segment CD Reflexive Property of Congruence
4. Angle ADC is a right angle Definition of Altitude
5. Angle BDC is a right angle Definition of Altitude
6. Angle ADC = Angle BDC All right angles are equal
7. Triangle ACD = Triangle BCD AAS Property of Congruence
8. Angle ACD = Angle BCD CPCTC
9. Segment CD bisects Angle BCD Definition of Bisected Angle
Note: CPCTC = Corresponding Parts of Congruent Triangles are Congruent.
Remember, an isosceles triangle has two equal sides and two equal base angles. Also, keep in mind that a bisected angle (one that is cut in half) has two equal parts.
So the basic course of action is:
1) Prove that triangle ACD is congruent to triangle BCD
2) From there, you can show that the corresponding parts of the triangles are congruent (in this case the top angles)
3) Since they are congruent, this means that they form a larger angle that has been bisected (a bisected angle tells us that the angle forms two smaller equal parts)