Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: \\( \overline { c k } \cong \overline { y j } \\) ; \\( \angle k \\) and \\( \angle j \\) are right angles; \\( \angle k \cong \angle j \\). prove: \\( \triangle c k y \cong \triangle y j c \\)

Explanation:

Step1: Identify the given information

We are given that \(\overline{CK}\cong\overline{YJ}\), \(\angle K\) and \(\angle J\) are right angles (so \(\angle K\cong\angle J\)), and \(CY = CY\) (common side).

Step2: Apply the Side - Angle - Side (SAS) criterion

In \(\triangle CKY\) and \(\triangle YJC\), we have:

• \(CK = YJ\) (given)
• \(\angle K=\angle J\) (given)
• \(CY = CY\) (common side)

By the Side - Angle - Side (SAS) congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

The Side - Angle - Side (SAS) postulate justifies that \(\triangle CKY\cong\triangle YJC\).