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In Fig.6.53,ABD is a triangle right angl...

In Fig.6.53,ABD is a triangle right angle at A and `AC_|_BD`.Show that
(i)`AB^2=BC.BD`.

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In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (ii) AC^2=BC.DC .

In Fig.6.53,ABD is a triangle right angle at A and AC_|_BD .Show that (iii) AD^2=BD.CD .

In Fig.6.59, ABC is a triangle in which angleABC<90^@ and AD_|_BC .Prove that AC^2=AB^2+BC^2-2BC.BD .

∆ABC is a right angled triangle right angled at A and AD _|_ BC . Prove that AD^2 = BD.CD .

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(i) AC^2=AD^2+BC.DM+((BC)/2)^2

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(ii) AB^2=AD^2-BC.DM+((BC)/2)^2

ABC is an isosceles triangle right angled at C.Prove that AB^2=2AC^2 .

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(iii) AC^2+AB^2=2AD^2+1/2BC^2

In Fig.6.58, ABC is a triangle in which angleABC>90^@ and AD_|_CB produced.Prove that AC^2=AB^2+BC^2+2BC.BD .

If Fig. 6.3 ,ABC and AMP are two right triangles right angled at B and M respectively.Prove that : (ii) (CA)/(PA)=(BC)/(MP)

R G PUBLICATION-TRIANGLES-EXERCISE
  1. Sides of triangle are given below.Determine which of them are right tr...

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  2. PQR is a triangle right angled at P and M is a point on QR such that P...

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  3. In Fig.6.53,ABD is a triangle right angle at A and AC|BD.Show that (i...

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  4. In Fig.6.53,ABD is a triangle right angle at A and AC|BD.Show that (i...

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  5. In Fig.6.53,ABD is a triangle right angle at A and AC|BD.Show that (i...

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  6. ABC is an isosceles triangle right angled at C.Prove thatAB^2=2AC^2.

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  7. ABC is an isosceles triangle with AC=BC.If AB^2=2AC^2.prove that ABC i...

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  8. ABC is an equilateral triangle of sides 2a.Find each of its altitudes.

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  9. Prove that the sum of the squares of the sides of a rhombus is equal t...

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  10. In Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC...

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  11. Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC an...

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  12. A ladder 10 m long reaches a window 8m above the ground. Find the dist...

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  13. A guy wire attached to a vertical pole of heigh 18 m is 24 m long and ...

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  14. An aeroplane leaves an airport and flies due north at a speed of 1000 ...

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  15. Two poles of heights 6 m and 11 m stand on a plane ground. If the dist...

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  16. D and E are points on the sides CA and CB respectively of a triangle A...

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  17. The perpendicular from A on side BC of atriangleABC intersects BC at ...

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

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  19. In an equilateral triangle, prove that three times the square of one s...

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  20. Tick the correct answer and a justify :In triangleABC,AB=6sqrt3,AC=12c...

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