Question

Prove That converse Pythagoras Therom And With Figure also ​

Answer 1

Answer:

a2 + b2 = c2

Proof of Pythagoras Theorem

Given: A ∆ XYZ in which ∠XYZ = 90°.

To prove: XZ² = XY² + YZ²

Construction: Draw YO ⊥ XZ

Proof: In ∆XOY and ∆XYZ, we have,

∠X = ∠X → common

∠XOY = ∠XYZ → each equal to 90°

Therefore, ∆ XOY ~ ∆ XYZ → by AA-similarity

⇒ XO/XY = XY/XZ

⇒ XO × XZ = XY²----------------- (i)

In ∆YOZ and ∆XYZ, we have,

∠Z = ∠Z → common

∠YOZ = ∠XYZ → each equal to 90°

Therefore, ∆ YOZ ~ ∆ XYZ → by AA-similarity

⇒ OZ/YZ = YZ/XZ

⇒ OZ × XZ = YZ² ----------------- (ii)

From (i) and (ii) we get,

XO × XZ + OZ × XZ = (XY² + YZ²)

⇒ (XO + OZ) × XZ = (XY² + YZ²)

⇒ XZ × XZ = (XY² + YZ²)

⇒ XZ² = (XY² + YZ²)

Answer 2

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