in the adjoining figure,ADis a median of triangle ABC If BL and CM are drawn perpendicularson AD produced, prove - Maths - Congruent Triangles

Question

in the adjoining figure,ADis a median of triangle ABC If BL and
CM are drawn perpendicularson AD produced, prove thatBL = CM

Priyanka Kedia · Accepted Answer

$G i v e n t h a t : A D i s a m e d i a n o f t r i a n g l e A B C a n d B L a n d C M a r e d r a w n p e r p e n d i c u l a r o n A D p r o d u c e d . T o \Pr o v e d : B L = C M \Pr o o f : I n Δ B L D a n d Δ C M D, B D = D C (g i v e n, A D i s m e d i a n) ∠ B L D = ∠ C M D (g i v e n, e a c h 90^{0}) ∠ B D L = ∠ C D M (v e r t i c a l l y o p p o s i t e a n g l e) \Rightarrow Δ B L D ≅ Δ C M D (b y A - S - A c o n g r u e n c e) T h u s, B L = C M (c . p . c . t .) h e n c e p r o v e d$

in the adjoining figure,ADis a median of triangle ABC. If BL and CM are drawn perpendicularson AD produced, prove thatBL = CM.