Question

1. given:

prove:
statements
1)
2)
3)
4)
5)
reasons
1.
2
3
4
5

Explanation:

Step1: Use the property of parallel lines

Since \( \overline{JK}\parallel\overline{MN}\), then \( \angle JKL=\angle MNL\) (alternate - interior angles).

Step2: Consider the given side - equality

We are given that \( \overline{JL}\cong\overline{ML}\).

Step3: Use the vertical - angles property

\(\angle JLK\) and \(\angle MLN\) are vertical angles, so \( \angle JLK\cong\angle MLN\).

Step4: Apply the ASA (Angle - Side - Angle) congruence criterion

In \(\triangle JKL\) and \(\triangle MNL\), we have:

• \(\angle JKL=\angle MNL\) (from Step 1)
• \(\overline{JL}\cong\overline{ML}\) (given)
• \(\angle JLK\cong\angle MLN\) (from Step 3)

By the ASA congruence criterion, \(\triangle JKL\cong\triangle MNL\).

Answer:

\(\triangle JKL\cong\triangle MNL\) (by ASA congruence criterion)