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M and N are point on sides QR and PQ res...

M and N are point on sides QR and PQ respectively of `/_\ PQR`, right-angled at Q. Prove that :
`PM^(2)+RN^(2)=PR^(2)+MN^(2)`

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M and N are mid- point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : PM^(2)+RN^(2)= 5 MN^(2) .

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P and Q are points on the sides C A and C B respectively of A B C , right-angled at C . Prove that A Q^2+B P^2=A B^2+P Q^2 .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

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In a right triangle A B C right-angled at C ,\ P and Q are the points on the sides C A and C B respectively, which divide these sides in the ratio 2:1 . Prove that 9AQ^2=9AC^2+4BC^2

In a right triangle A B C right-angled at B , if P a n d Q are points on the sides A Ba n dA C respectively, then (a) A Q^2+C P^2=2(A C^2+P Q^2) (b) 2(A Q^2+C P^2)=A C^2+P Q^2 (c) A Q^2+C P^2=A C^2+P Q^2 (d) A Q+C P=1/2(A C+P Q)dot

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NAGEEN PRAKASHAN ENGLISH-TRIANGLES -Exercise 6d
  1. triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) ...

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  2. In an equilateral triangleABC, AD is the altitude drawn from A on the ...

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  3. M and N are point on sides QR and PQ respectively of /\ PQR, right-an...

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  4. The given figure shows a triangle ABC, in which AB gt AC. E is the mi...

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  5. In a square ABCD, show that AC^(2) = 2AB^(2).

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  6. In a rhombus ABCD, prove that AC^(2) + BD^(2) = 4AB^(2)

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  7. In triangle ABC, angle A =90^(@), CA=AB and D is a point on AB produce...

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  8. In acute angled triangle ABC, AD is median and AE is altitude , prove...

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  9. The following figure shows a triangle ABC in which AD is a median and ...

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  10. From a point O in the interior of a A B C , perpendiculars O...

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  11. In an acute angled triangle ABC, AD is the median in it. then : AD^...

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  12. In a right triangle ABC, right angled at A, AD is drawn perpendicular ...

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  13. In the given figure , ABC is a right triangle, right angled at B. Medi...

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  14. In the given figure , angleQPR= 90^(@) QR = 26 cm PM = 6cm, MR = 8c...

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  15. Given a right angled triangleABC. The lengths of the sides containing ...

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  16. In an acute-angled triangle, express a median in terms of its sides...

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

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  18. A B C is a right triangle right-angled at Ca n dA C=sqrt(3)B C . Prove...

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  19. In triangleABC , angleA= 60^(@) prove that BC^(2)= AB^(2)+AC^(2)- AB ....

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  20. In the adjoining figure, find x,y and h.

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