Question

State and prove Pythagoras theorem. Also solve the sum , determine whether the triangle having sides ( a-1) cm, 2√acm and (a+1) cm is a right angled triangle.

Answer 1

Answer:

Step-by-step explanation:

Pythagoras theorem:

In  aright angle triangle the square of the hypotenuse is equal to the sum of the square of the other two sides

Proof: In the figure ABC is a right angle triangle.here AC is the hypotenuse

Let us draw BD ⊥ AC.

In ΔABC and Δ ABD

∠ABC=∠ADC=90

∠ABD=90-∠A=∠C

∠A is common

So ΔABC and Δ ABD are similar

So AC/AB=AB/AD

So AB²=AC*AD....................(1)

Similarly ΔABC and Δ ADC are similar

So AC/BC=BC/DC

BC²=AC*DC.............................(2)

Adding (1) and (2) we get

AB²+BC²=AC*AD+AC*DC

= AC( ADDC)=AC*AC=AC²

Thus AC²=AB²+BC²

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Let the side of the triangle are

x=a-1 cm, y=2√a cm, z=a+1

x²+y²=(a-1)²+(2√a)²=a²-2a+1+4a

=a²+2a+1=(a+1)²=z²

So x²+y²=z²

Thus the formed triangle is a right angle triangle