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P is any point inside the rectangle ABCD. Prove that `AP^2+CP^2=BP^2+DP^2`

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O is any point inside a rectangle ABCD. Prove that OB^2+OD^2=OA^2+OC^2 .

If D is the middle point of the side BC of the triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + DC^2) .

P and Q are points on the sides CA and CB of a ∆ABC , right angled at C. Prove that AQ^2 + BP^2 = AB^2 + PQ^2 .

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4BP^2 = 4 BC^2 + AC^2

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4 (AQ^2 + BP^2) = 5 AB^2

The sides of the quadriIateraI ABCD are not equal to one another and AC_|_BD prove that AB^2+CD^2=AD^2+BC^2

ABC and DBC are two right angled triangles with common hypotenuse BC with their sides AC and BD intersecting at P. Prove that: AP×PC=DP×PB .

E is any point on the side BC of the parallelogram ABCD. AE intersects the diagonal BD at point F. Prove that DF×EF=FB×FA .

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R G PUBLICATION-TRIANGLES-EXERCISE
  1. P is any point inside the rectangle ABCD. Prove that AP^2+CP^2=BP^2+DP...

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  2. All circles are . (congruent, similar)

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  3. All squares are -. (Similar, congruent)

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  4. All triangles are similar. (isosceles, equilateral)

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  5. Two polygons of the same number of sides are similar, if(a) their corr...

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  6. Two polygons of the same number of sides are similar, if(b) their corr...

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  7. Give two different examples of pair of(i) similar figures

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  8. Give two different examples of pair of((ii) non-simiIar figures

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  9. State whether foIIowing quadrilaterals are similar or not:

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  10. In fig(i) ,DE||BC.Find EC in (i).

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  11. E and F are points on the sides PQ and PR respectively of a trianglePQ...

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  12. E and F are points on the sides PQ and PR respectively of a trianglePQ...

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  13. E and F are points on the sides PQ and PR respectively of a trianglePQ...

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  14. In Fig. , if LM||CB and LN||CD,prove that (AM)/(AB)=(AN)/(AD)

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  15. In Fig. DE||AC and DF||AE.Prove that (BF)/(FE)=(BE)/(EC)

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  16. In Fig. 6.20, DE||OQ and DF||OR.Show that EF||QR.

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  17. In Fig., A, B and C are points on OP, OQ and OR respectively such that...

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  18. Using Theorem 6.1, prove that a line drawn through the mid-point of on...

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  19. Using Theorem 6.2, prove that the line joining the mid-points of any t...

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  20. ABCD is a trapezium in which AB||DCand its diagonals intersect each ot...

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  21. The diagonals of a quadrilateral ABCD intersect each other at the poin...

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