Question

problem 24
given: parallelogram spqt,
\\( \overline { p k } \cong \overline { t l } \\)
prove: \\( \angle p s k \cong \angle t q l \\)

1. click here to insert
2. \\( \overline { p k } \cong \overline { t l } \\)
3. click here to insert

4.
click here to insert

1. given

6.

Explanation:

Step1: Properties of parallelogram

In parallelogram \(SPQT\), \(SP\parallel QT\). So, \(\angle SPK=\angle TQL\) (alternate interior angles).

Step2: Congruent triangles

We know that \(SP = QT\) (opposite sides of a parallelogram are equal), \(\overline{PK}\cong\overline{TL}\) (given), and \(\angle SPK=\angle TQL\) (from step 1). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle SPK\cong\triangle TQL\).

Step3: Corresponding angles

Since \(\triangle SPK\cong\triangle TQL\), \(\angle PSK\cong\angle TQL\) (corresponding parts of congruent triangles are congruent).

Answer:

\(\angle PSK\cong\angle TQL\)