Question

11/14 - triangle congruence schoology assignment
possible points: 0.58
what other information, if any, do you need to prove the two triangles congruent by sas? explain.
choose the correct answer below.
○ a. \\( \overline { g t } \cong \overline { n q } \\) is needed because the congruent angles need to be included between two corresponding congruent sides.
○ b. \\( \overline { g l } \cong \overline { n m } \\) is needed because the congruent angles need to be included between two corresponding congruent sides.
○ c. \\( \overline { g t } \cong \overline { n q } \\) and \\( \overline { g l } \cong \overline { n m } \\) are both needed because all three corresponding sides must be congruent.
○ d. no additional information is needed to prove the triangles congruent by sas.
a.
b.
c.
d.

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that for two triangles to be congruent by SAS, two sides and the included angle of one triangle must be congruent to two sides and the included angle of the other triangle.

Step2: Analyze the given triangles

In \(\triangle LTG\) and \(\triangle MQN\), we know that \(LT = MQ\) (given by the tick marks). The angles \(\angle T\) and \(\angle Q\) are the angles. For SAS, we need the sides adjacent to the angles to be congruent. The sides adjacent to \(\angle T\) in \(\triangle LTG\) is \(GT\), and the side adjacent to \(\angle Q\) in \(\triangle MQN\) is \(NQ\).

Answer:

A. \(\overline{GT}\cong\overline{NQ}\) is needed because the congruent angles need to be included between two corresponding congruent sides.