Question

1. given: \\( \overline { k l } \parallel \overline { n p } \\), \\( \overline { k l } \cong \overline { n p } \\) prove: \\( \triangle k m l \cong \triangle p m n \\)

Explanation:

Step1: Vertical angles

$$\angle KML=\angle PMN$$ (Vertical angles are congruent)

Step2: Alternate interior angles

Since \(KL\parallel NP\), then \(\angle K=\angle P\) (Alternate interior angles are congruent)

Step3: Given

\(KL = NP\) (Given)

Step4: ASA congruence

By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle KML\cong\triangle PMN\)

Answer:

1. \(\angle KML=\angle PMN\); Vertical angles are congruent
2. \(\angle K=\angle P\); \(KL\parallel NP\), Alternate interior angles are congruent
3. \(KL = NP\); Given
4. \(\triangle KML\cong\triangle PMN\); ASA (Angle - Side - Angle) congruence