Question

use the figure on the right to find the length of (overline{dc}).

Explanation:

Step1: Recall the property of a kite

In a kite, the diagonals are perpendicular. Also, in the given kite \(ABCD\), \(AD = AB = 10\). Since the diagonals of a kite are perpendicular (\(AC\perp BD\)) and \(DE=EB\) (one of the diagonals is bisected by the other).

Step2: Use the property of congruent triangles

Triangles \( \triangle AED\) and \( \triangle AEB\) are right - angled triangles (\(\angle AED=\angle AEB = 90^{\circ}\)), \(AD = AB\) (given \(AD = AB=10\)) and \(AE = AE\) (common side). By the Hypotenuse - Leg (HL) congruence criterion, \(\triangle AED\cong\triangle AEB\). Similarly, \(\triangle DEC\cong\triangle BEC\).

Step3: Calculate the length of \(DC\)

Since \(AD = AB = 10\) and the figure is a kite, \(DC=BC\). Given \(BC = 10\), so \(DC=10\)

Answer:

\(10\)