Use the given information to make a neat diagram of the figure having given properties and write down the name of the figure.
In triangle $A B C,$ $A B^{2} = B C^{2} + A C^{2}$ and $A C = 2 B C .$

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Solution

Ref Above Image
Given $A B^{2} = A C^{2} + B C^{2}$ .
Hence $Δ A B C$ is right angled triangle (right angle at $C$ )

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In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC² = AB² + BC² − 2BC.BD.

In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC² = AB² + BC² + 2BC.BD.

A B C

A D ⊥ B C

{A C}^{2} + {A B}^{2} + {B C}^{2} + 2 B C - B D

∠ B

△ A B C

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{A C}^{2} - {A B}^{2} - {B C}^{2} + 2 B C . B D

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