Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: quadrilateral rstu;
\\( \overline { r s } \cong \overline { u t } \\) and \\( \overline { s t } \cong \overline { r u } \\) prove: \\( \delta r s t \cong \delta t u r \\)

Explanation:

Step1: Identify the sides of the triangles

We have \(\triangle RST\) and \(\triangle TUR\).
In \(\triangle RST\) and \(\triangle TUR\):

• \(RS\cong UT\) (given)
• \(ST\cong RU\) (given)
• \(RT = RT\) (common side, reflexive property of congruence: \(a=a\) for any geometric figure \(a\))

Step2: Apply the congruence criterion

By the Side - Side - Side (SSS) congruence criterion. If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
For \(\triangle RST\) and \(\triangle TUR\), since \(RS\cong UT\), \(ST\cong RU\) and \(RT\cong RT\), we can say \(\triangle RST\cong\triangle TUR\)

Answer:

The SSS (Side - Side - Side) congruence theorem justifies that \(\triangle RST\cong\triangle TUR\)