In the figure ( 2 ) given below, A B C is right-angled triangle at A. AGFB is a square on the side A B and B C D E is a square on the hypotenuse BC. If A N \perp  ED, prove that:(i) \Delta \mathbf{B} \mathbf{C} \mathbf{F} \cong \Delta \mathbf{A} \mathbf{B} \mathbf{E}(ii) area of square ABFG = area of rectangle BENM.

Foundation

Mathematics Foundation

Properties of Area of Parallelogram

Basic Properties of Quadrilateral

Congruency of Triangles

Question

In the figure ( 2 ) given below,

A B C

is right-angled triangle at A. AGFB is a square on the side

A B

and

B C D E

is a square on the hypotenuse BC. If

A N \perp&nbsp; ED

, prove that:
(i)

Δ B C F ≅ Δ A B E

(ii) area of square ABFG = area of rectangle BENM. Question Image

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Given:
ABC is a right-angled triangle at A.
Squares AGFB and BCDE are drawn on the side AB and hypotenuse BC of

From

and rectangle BENM

ar (rectangle BENM)

ar (rectangle BENM)
Hence proved.