Question

ghlj and gstu are both parallelograms. why is
$\angle l \cong \angle t$?

Explanation:

Step1: Properties of parallelograms

In a parallelogram, opposite angles are congruent. For parallelogram \(GHLJ\), \(\angle L\cong\angle G\). For parallelogram \(GSTU\), \(\angle T\cong\angle G\).

Step2: Transitive property of congruence

If \(\angle L\cong\angle G\) and \(\angle T\cong\angle G\), then by the transitive property of congruence (if \(a = b\) and \(b = c\), then \(a = c\)), \(\angle L\cong\angle T\).

Answer:

Since in parallelogram \(GHLJ\), \(\angle L\cong\angle G\) (opposite angles of a parallelogram are congruent) and in parallelogram \(GSTU\), \(\angle T\cong\angle G\) (opposite angles of a parallelogram are congruent), by the transitive property of congruence, \(\angle L\cong\angle T\).