Question

1. given: \\( \overline { l t } \cong \overline { t r } \\), \\( \angle l t \cong \angle e t r \\), \\( i t \parallel e r \\) prove: \\( \triangle l i t \cong \triangle t e r \\)

Explanation:

Step1: Use the property of parallel lines

Since \(IT\parallel ER\), by the alternate - interior angles theorem, \(\angle LIT=\angle TER\).

Step2: Apply the ASA (Angle - Side - Angle) congruence criterion

We are given that \(\overline{LT}\cong\overline{TR}\) (side), \(\angle ILT\cong\angle ETR\) (angle), and from Step 1 \(\angle LIT=\angle TER\) (angle).
By the ASA congruence criterion, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Answer:

\(\triangle LIT\cong\triangle TER\) by the ASA (Angle - Side - Angle) congruence criterion.