We can first prove that △KLG is congruent to △KDE.
K is the mid point of LD, which means LK and KD has same length.
LK = KD (given)
Both angle KLG and KDE is same.
KLG = KDE = 90° (given)
As △GKE is isosceles triangle, GK and KE must be the same length, this is a property of isosceles triangle.
GK = KE (sides. Opp. Eq. Angles.)
With these three proves, we can prove that △KLG is congruent to △KDE. (Rhs)
Now, finally we can prove that LG is congruent to DE, since △KLG is congruent to △KDE, all sides and angles are same. Abbreviation: (corr. Sides. Congruent △s)
