Consider the figure, Point \(Y\) is the midpoint of \(IL\) and \(JK\). What can one say about the measures \(IJ\) and \(KL\)?
Solution:
From the figure, consider two triangles \(\Delta IYJ\) and \(\Delta LYK\).
We now have:
\(IY =\) (Since \(Y\) is the midpoint of \(IL\))
\(\angle IYJ = \angle LYK\) ()
\(JY =\) (Since \(Y\) is the midpoint of \(JK\))
By congruence condition, the two triangles are congruent.
The corresponding vertices are
Vertex \(Y\) \(\leftrightarrow \) Vertex .
Vertex \(I\) \(\leftrightarrow \) Vertex .
Vertex \(J\) \(\leftrightarrow \) Vertex .
Hence
Since the triangles are congruent, their corresponding are equal by CPCT.
Therefore, \(IJ = LK\).
Hence, \(IJ\) and \(KL\) are in length.