Q. 384.2( 19 Votes )

# If a line is draw

Answer :

Given: In Δ ABC, AB which intersects AB and AC at D and F respectively.

To Prove: Construction:

Join B, E and C, D and then draw DM AC and EN AB. Proof:

Area of Δ ADE Area of Δ BDE So  … (2)

Again, area of Δ ADE Area of Δ CDE So  …(3)

Observe that Δ BDE and Δ CDE are on the same base DE and between same parallels BC and DE.

So, ar(Δ BDE) = ar(Δ CDE) … (3)

From (1), (2) and (3), we have Hence, proved.

OR

Statement: In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Given: A right triangle ABC right angled at B.

To Prove: AC2 = AB2 + BC2

Construction: Draw BD AC Proof:

We know that if a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Δ ADB ~ Δ ABC

So, Or AD × AC = AB2 … (1)

Also, Δ BDC ~ Δ ABC

So, Or CD × AC = BC2 … (2)

Adding (1) and (2),

AD × AC + CD × AC = AB2 + BC2

AC (AD + CD) = AB2 + BC2

AC2 = AB2 + BC2

Hence, proved.

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