19. In the figure, BAC = 90, AD ⊥ BC. Prove that : AB2 + CD2 = BD2 + AC2.
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Answered by
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Draw AD ⊥ to BC
ΔADB and ΔADC are formed
In ΔADB
AB²=AD²+BD²
In ΔADC
AC²=AD²+CD²
subtracting both equation we get
AB²-AC²= AD²+BD²-AD²-CD²
AB²-AC²=BD²-CD²
proved
ΔADB and ΔADC are formed
In ΔADB
AB²=AD²+BD²
In ΔADC
AC²=AD²+CD²
subtracting both equation we get
AB²-AC²= AD²+BD²-AD²-CD²
AB²-AC²=BD²-CD²
proved
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