\(KLMN\) is a quadrilateral in which \(KN = LM\) and \(∠ NKL = ∠MLK\).
Demonstrate that:
(i) \(∆ KLN≅ ∆ LKM\)
(ii) \(LN= KM\)
(iii) \(∠ KLN= ∠ LKM \).
Proof:
(i) Considering two triangles \(ΔKLN\) and \(ΔLKM\).
Here, \(KN =\) [Given] ----(1)
\(∠ NKL = ∠\) [Given] ---(2)
\(KL=KL\) [Common side] ---(3)
Therefore, by congruence rule\(ΔKLN ≅ ΔLKM\)
Hence, we proved.
(ii) Since \(ΔKLN ≅ Δ\) [By SAS Congruence rule]
So, by , \(LN = KM\)
Hence, we proved.
(iii) Since \(ΔKLN ≅ ΔLKM\) [By SAS Congruence rule]
So, by \(∠KLN= ∠LKM\)
Hence, we proved.