Geometry

Question Analysis:
This question involves two triangles that share a side and have congruent angles.
We need to use the congruence of triangles to find the length of side DC based on the given information.

Key Concept Explanation:
We know that AB = AD (given side), $\angle BAC=\angle DAC$ (given angle), and AC is a common side to both triangles.
Therefore, triangle ABC and triangle ADC must be congruent by the SAS (Side-Angle-Side) postulate.

Step-by-Step Solution:
Identify the given information:
AB = AD
∠BAC = ∠DAC
AC = AC
BC = 10
Apply congruence:
Since AB = AD and the angles ∠BAC and ∠DAC are congruent, triangles ABC and ADC are congruent by the SAS postulate (side, angle, side).
Conclude that...