Answer:
Option d is correct.
Vertical angles are congruent;
SAS
Step-by-step explanation:
Given: \(JK \cong KL\) , \(NK \cong KM\)
In ΔNKJ and ΔMLK
\(JK \cong KL\) and [Side] {Given}
\(NK \cong KM\)
Vertical angles states that the two lines intersect to make an X, angles on opposite sides of the X are called vertical angles.
i.e \(\angle NKJ\) and \(\angle MKL\) are vertical angles.
Also, vertical angles are congruent.
\(\angle NKJ \cong \angle MKL\) [Angle] [Vertical angles are congruent]
SAS(Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
then, by SAS postulates;
\(\triangle NKJ \cong \triangle MLK\) Hence proved!
Therefore:
Statement Reason
1. \(JK \cong KL\), \(NK \cong KM\) Given
2. \(\angle NKJ \cong \angle MKL\) Vertical angles are congruent
3. \(\triangle NKJ \cong \triangle MLK\) SAS
