Question

a diagram is shown where point l is the midpoint of \\( \overline { b k } \\), \\( \overline { l w } \cong \overline { l t } \\), and \\( \angle w l b \cong \angle t l k \\).
use the given information to answer the questions about the incomplete proof that is shown.

1. \\( \overline { l w } \cong \overline { l t } \\) 1. given
2. \\( \angle w l b \cong \angle t l k \\) 2.
3. l is the midpoint of \\( \overline { b k } \\) 3. given
4. 4.
5. \\( \triangle w b l \cong \triangle \\) 5.

Explanation:

Step1: Determine the reason for $\angle WLB\cong\angle TLK$

Since it is given in the problem statement, the reason is "Given".

Step2: Find the congruent segments from the mid - point

If \(L\) is the mid - point of \(\overline{BK}\), then by the definition of a mid - point, \(\overline{BL}\cong\overline{KL}\).

Step3: Determine the congruent triangles

We have \(\overline{LW}\cong\overline{LT}\) (Given), \(\angle WLB\cong\angle TLK\) (Given), and \(\overline{BL}\cong\overline{KL}\) (from the mid - point definition). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle WBL\cong\triangle TKL\).

Answer:

1. Given; 4. \(\overline{BL}\cong\overline{KL}\), Definition of mid - point; 5. \(TKL\), SAS (Side - Angle - Side)