5. In a right angled triangle if perpendicular is drawn from the right angle to the hypotenuse then prove that the area of the square on the perpendicular is equal to the area of the rectangle formed on the two segments of the hypotenuse

6. P is the mid -point of the side AD of the parallelogram ABCD. Straight line BP intersect the diagonal AC at R and the side CD at Q. Prove that QR=2RB

7. In an isosceles triangle ABC with AB =AC, BD is perpendicular from B to the side AC .Prove that

BD^2-CD^2=2CD^2.AD

8. In a triangle ABC, AD is perpendicular to BC. Prove that AB^2 +CD^2=AC^2+DB^2

9. In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides prove. Determine the length of in terms of b and c

10. In a triangle PQR, PD is perpendicular to QR such that D lies on QR. If PQ=a, PR=b, QD=c and DR=d, prove that (a +b) (a -b) =(c +d) (c -d)

11. In a quadrilateral ABCD, angle A+ angle D=90degree. Prove that AC^2+BD^2=AD^2+BC^2

12. D is the midpoint of side BC of triangle ABC. AD is bisected at point E and BE produced cuts AC at the point X. Prove that BE: EX=3:1

13. In triangle ABC, AD is the median, X is a point on AD such that AX:XD=2:3 .Ray BX intersects AC in Y. Prove that BX=4XY

14. In quadrilateral ABCD given that

Angle A + angle D=90 degree

Prove that AC^2+BD^2=AD^2+BC^2