Question

use the given property to complete the statement. transitive property of congruence if ( overline{xy} cong overline{zv} ) and ( overline{zv} cong overline{uv} ), then ____. ( overline{zv} cong overline{uv} ) ( overline{xy} cong overline{zv} ) ( overline{zv} cong overline{zv} ) ( overline{xy} cong overline{uv} )

Explanation:

Step1: Recall the transitive property of congruence

If \(a\cong b\) and \(b\cong c\), then \(a\cong c\).

Step2: Apply the property to the given segments

Here, \(a = \overline{XY}\), \(b=\overline{ZV}\), \(c=\overline{UV}\). Since \(\overline{XY}\cong\overline{ZV}\) and \(\overline{ZV}\cong\overline{UV}\), by the transitive property of congruence, \(\overline{XY}\cong\overline{UV}\).

Answer:

$\overline{XY}\cong\overline{UV}$