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Question
In the adjacent figure, △ ABC, D is the midpoint of BC. DE⊥ AB, DF⊥ AC and DE = DF. Show that △ BED ≅△ CFD
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Solution
Given that D is the midpoint of BC of △ABC.
DF⊥AC;DE=DF
DE⊥AB
In △BED and △CFD
∠BED=∠CFD (given as 90∘)
BD=CD (∴D is mid point of BC)
ED = FD (given)
∴△BED≅△CFD (RHS congruence)
DF⊥AC;DE=DF
DE⊥AB
In △BED and △CFD
∠BED=∠CFD (given as 90∘)
BD=CD (∴D is mid point of BC)
ED = FD (given)
∴△BED≅△CFD (RHS congruence)
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