Question

in fig BD perpendicular to BC DE perpendicular to AB and AC perendicular to BC ,prove that BE/DE=AC/BC​

Answer 1

Step-by-step explanation:

BD and AC are perpendicular to the same line BC

therefore, BD//AC then BA is the transversal

now, angle DBA= angle BAC (SINCE VERTICALLY OPPOSITE ANGLES)

THUS, in ∆ DAB and in ∆ ACB, we have,

angle DBE=angle BAC

and angle DEB= angle ACB=90°

THUS ∆DEB ~∆ACB (by AA)

THEN,

BE/AC=DE/BC

OR, BE/DE=AC/BC

HENCE PROVED.

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