Question

in the figure, np = nj and m∠ypn = m∠kjn. complete the statement.△pny ≅ △______
options: jkn, kjy, nkj, jnk

Explanation:

Step1: Identify Given Information

We know \( NP = NJ \) and \( m\angle YPN = m\angle KJN \). Also, \( \angle PNY \) and \( \angle JNK \) are the same angle (common angle at \( N \)).

Step2: Apply ASA Congruence Criterion

For triangles \( \triangle PNY \) and \( \triangle JNK \):

• \( NP = NJ \) (given)
• \( \angle YPN = \angle KJN \) (given)
• \( \angle PNY = \angle JNK \) (common angle)

By Angle - Side - Angle (ASA) congruence postulate, \( \triangle PNY \cong \triangle JNK \).

Answer:

\(\triangle PNY \cong \triangle JNK\) (Option: JNK)