- Prove that any median of a triangle divides the triangular region into two regions
of equal area.
- A parallelogram and a rectangular region of equal area lie on the same side of the
bases. Show that the perimeter of the pa rallelogram is greater than that of the
rectangle.
- Xand Y are the mid points of the sides AB and AC of the triangle ABC. Prove that
the area of the triangular region AXY =
4
1
(area of the triangular region ABC)
- In the figure, ABCD is a trapezium with sides AB and CD parallel. Find the area
of the region bounded by the trapezium ABCD.
11.P is any point interior to the parallelogram ABCD. Prove that the area of the
triangular region PAB + the area of the triangular region PCD =
2
1
(area of the
parallelogram ABCD).
- A line parallel to BC of the triangle ABC intersects ABandACatD and E
respectively. Prove that the area of the triangular region DBC = area of the
triangular region EBC and area of the triangular region DBF = area of the
triangular region CDE.
- A 1 right angle of the triangle ABC. D is a point on AC. Prove that
BC^2 AD^2 BD^2 AC^2.
- ABC is an equilateral triangle and AD is perpendicular to BC. Prove that
4 AD^2 3 AB^2.
15.ABC is an isosceles triangle. BC is its hypotenuse and P is any point on BC.
Prove that PB^2 PC^2 2 PA^2.
- C is an obtuse angle of 'ABC;AD is a perpendicular to BC. Show that.
AB^2 = AC^2 + BC^2 + 2BC.CD
- C is an acute angle of 'ABC ;AD is a perpendicular to BC. Show that
AB^2 AC^2 BC^2 2 BC.CD.
- AD is a median of 'ABC. Show that, AB^2 AC^2 2 (BD^2 AD^2 ).
