CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sine Rule

State the con...

Question

State the converse of Pythagoras' Theorem and prove it.

Open in App

Solution

Statement : If a right triangle, the square of the hypotenuse is equal to the sum of the square of other two sides.
$\begin{matrix} G i v e n Δ A B C r i g h t a n g l e a t B T o p r o v e - A C^{2} = A B^{2} + B C^{2} C o n s t r u c t i o n : D r a w B D ⊥ A C o o f : sin c e B D ⊥ A C B y u sin g t h e o r e m - i f a p e r p e n d i c u l a r i s d r a w n f r o m t h e v e r t e x o f t h e r i g h t a n g l e o f t h e a r i g h t t r i a n g l e t o t h e h y p o t e n u s e t h e n t r i a n e o n b o t h s i d e o f t h e p e r p e n d i c u l a r a r e s i m i l a r t o w h o l e t r i a n g l e a n d t o e a c h o t h e r . Δ A B D \sim Δ A B C sin c e, s i d e s o f s i m i l a r t r i a n g l e s a r e i n t h e s a m e r a t i o \Rightarrow \frac{A D}{A B} = \frac{A B}{A C} \Rightarrow A D . A C = A B^{2} - - - - (1) s i m i l a r l y Δ B D C \sim Δ A B C sin c e, s i d e s o f s i m i l a r t r i a n g l e s a r e i n t h e s a m e r a t i o \Rightarrow \frac{C D}{B C} = \frac{A B}{A C} \Rightarrow C D . A C = B C^{2} - - - - (2) N o w, a d d i n g (1 + 2) w e g e t A D . A C + C D . A C = A B^{2} + B C^{2} A C (A D + C D) = A B^{2} + B C^{2} A C \times A C = A B^{2} + B C^{2} ∴ A B^{2} + B C^{2} = A C^{2} p r o v e d . \end{matrix}$

Suggest Corrections

thumbs-up

3

Similar questions

Q. Write converse of Pythagoras theorem and prove it.

Q. Write the converse of the Pythagoras Theorem and prove it.

State the converse of Pythagoras' theorem.

Q. State and prove Pythagoras theorem.

Q. State converse of Pythagoras theorem.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sine Rule

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon