Question

10. Through the vertex A of triangleARC, a linel is drawn. BM and CN are perpendiculars drawn on LIFO is
the mid-point of BC, show that OM = ON​

Answer 1

Step-by-step explanation:

l is a straight line passing through the vertex A.

BM⊥l and CN⊥l.

L is the mid-point of BC

Draw OL⊥l

If a transversal make equal intercepts on three or more parallel lines, then any other transversal intersecting them will also make equal intercepts.

BM⊥l, CN⊥l and OL⊥l.

∴ BM∥OL∥CN

Now, BM∥OL∥CN and BC is the transversal making equal intercepts.

i.e. BL=LC.

∴ The transversal MN will also equal intercepts.

⇒ OM=ON

In △LM and △LNO,

⇒ OM=ON

⇒ ∠LOM=∠LON [ OL is perpendicular to BC ]

⇒ OL=OL [ Common line ]

∴ △LMO≅△LNO [ By SAS congruence theorem ]

⇒ LM=LN [ By C.P.C.T ]

Answer 2

Answer:

Hope it help to you ..................

Step-by-step explanation:

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