Answer :

Given: ABC is a triangle with XY || AC divides the triangle into two parts equal in areas.

To find:

Proof:

ar ΔBXY = ar trap. XYCA (Given) ∴ ar ΔBXY = ar ΔABC

In ΔBXY andBAC,

∠BXY = ∠BAC (Corresponding angles)

∠BYX = ∠BCA (Corresponding angles)

ΔBXY ∼ ΔBAC (AA similarity)

∴ = (Areas of similar triangle)

∴ =

∴ =

∴ AB – BX = √ 2 BX – BX

∴ AX = (√ 2 – 1)BX

= =.

To find:

Proof:

ar ΔBXY = ar trap. XYCA (Given) ∴ ar ΔBXY = ar ΔABC

In ΔBXY andBAC,

∠BXY = ∠BAC (Corresponding angles)

∠BYX = ∠BCA (Corresponding angles)

ΔBXY ∼ ΔBAC (AA similarity)

∴ = (Areas of similar triangle)

∴ =

∴ =

∴ AB – BX = √ 2 BX – BX

∴ AX = (√ 2 – 1)BX

= =.

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