Question

objective/aim
Related Knowledge,

• Materials Required,

• Procedure,

• Observations,

• Conclusion.
to verify “ PYTHAGORAS THEOREM” for a given right angled triangle.​

Answer 1

Answer:

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Step-by-step explanation:

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

Given: We are given a right triangle ABC right angled at B.

To prove: AC²=AB²+BC²

Construction: Draw BD parallel to AC.

Proof: In triangles ADB and ABC, we have

Angle ADB = Angle ABC    (Each 90⁰)

and, Angle A = Angle A      (Common)

So, ΔABD is similar to ΔABC    (AA similarity criterion)

⇒ AD/AB = AB/AC    (In similar triangles corresponding sides are proportional)

⇒ AB²=AD*AC            ---(1)

In triangle BDC and ABC, we have

Angle CDB = Angle ABC    (Each 90⁰)

Angle C = angle C  (Common)

So, ΔBDC is similar to ΔABC    (In simialr triangles corresponding sides are proportional)

⇒DC/BC=BC/AC

⇒BC²=AC*DC      ---(2)

Adding equations 1 and 2, we get

AB²+BC²=AD*AC+AC*DC

⇒AB²+BC²=AC(AD+DC)

⇒AB²+BC²=AC²

Hence, AC²=AB²+BC²

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