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Theorem 6.8 : In a right triangle, the s...

Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

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Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Use the above theorem, in the following. If ABC is an equilateral triangle with AD bot BC , then prove that AD^(2) = 3DC^(2) .

(Pythagoras's Theorem) Prove by vector method that in a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(Pythagorass Theorem) Prove by vector method that in a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.

PYTHAGORAS THEOREM : In a Right angled triangle; the square of hypotenuse is equal to the sum of the squares of the other two sides.

Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. Using the above, do the following: Prove that, in a DeltaABC , if AD is perpendicular to BC, dien AB^(2) + CD^(2) = AC^(2) + BD^(2) .

Prove that is a right angle triangle, the square of the hypotenuse is equal the sum of the squares of other two sides.

STATEMENT In a right triangle the square of the hypotenuse equals the sum of the squares of its remaining two sides.

In order to prove, 'In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides (i) Draw a near labelled figure. (ii) Write 'Given' and 'To Prove' from the figure drawn by you.

Theorem 6.9 : In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

In aright angled triangle,the square of the hypotenuse is equal to to the sum of squares on the other two sides,prove.Using the above theorem,determine the length of AD in terms of b and c.

CBSE COMPLEMENTARY MATERIAL-TRIANGLE-Short Answer Type Questions-II
  1. Theorem 6.8 : In a right triangle, the square of the hypotenuse is equ...

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  2. In the given figure, (QR)/(QS)= (QT)/(PR) and angle1 = angle2 then pro...

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  3. In equilateral triangleABC, ADbotBC. Prove that 3BC^2= 4AD^2.

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  4. In the given figure angleABC=90^(@) and CD bot AB. Prove that (BC^(2)...

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  5. In Fig. 4.179, A B C and D B C are on the same base B C . If A...

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  6. If AD and PS are medians of triangleABC and trianglePQR respectively w...

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  7. In the given figure, DE || AC. Which of the following is correct? x=(...

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  8. Prove that the sum of the squares of the sides of a rhombus is equa...

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  9. A street light bulb is fixed on a pole 6 m above the level of the stre...

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  10. Two poles of height a metres and b metres are p metres apart. Prove th...

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  11. In the given figure AB || PQ || CD, AB=x, CD=y and PQ=z. Prove that 1/...

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  12. In the given figure (PS)/(SQ)=(PT)/(TR) and anglePST = anglePRQ. Prove...

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  13. In the figure, a point O inside triangleABC is joined to its vertices....

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  14. Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, ...

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  15. The Hypotenuse of a right triangle is 25 cm and out of the remaining t...

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  16. In the given figure DE || AC and (BE)/(EC)=(BC)/(CP). Prove that DC |...

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  17. In a quadrilateral ABCD, angleB=90^(@) and AD^(2)= AB^(2) + BC^(2)+CD^...

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  18. In the given figure, DE || BC, DE= 3 cm, BC = 9 cm and ar (DADE) = 30c...

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  19. In an equilateral triangle ABC, D is a point on side BC such that B D=...

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  20. Ii DeltaPQR, PDbotQR such that D lies on QR, if PQ=a,PR=b,QD=c and DR=...

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  21. The ratio of the the areas of two similar triangles is equal to the ra...

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