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  • In the given figure, AD is a median of 3ABC. If BL and CM are drawn perpendiculars on AD and AD produced. <img alt="" src="https://cdn.entrance360.com/media/uploads/2020/07/11/t18.png" st

In the given figure, AD is a median of 3ABC. If BL and CM are drawn perpendiculars on AD and AD produced.

Then,

Option: 1

LD = DM


Option: 2

BL = CM


Option: 3

Both (a) and (b)


Option: 4

None of the above


Answers (1)

best_answer

\\\text{In right triangles } \Delta B L D\text{ and } \triangle C M D,\text{ we have} \\\\B D=C D \qquad[\because D \text { is the midpoint of } B C]\\\\ \angle B L D=\angle C M D \quad\left[\text { each equal to } 90^{\circ}\right] \\\\ \angle B D L=\angle C D M \quad[\text { vert. opp } \angle_S] \\\\ \therefore \quad \Delta B L D \cong \Delta C M D \quad\text { [AAS-criteria] } \\\\ \text{Hence, } B L=C M \quad\text{ and }\quad D L=D M \quad [\text { c.p.c.t. }]

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