1. Sides AB, AC and median AD of AABC are
respectively proportional to sides PQ, PR and median
PM of another APQR. Show that AABC - APOR.
2. ABC is a triangle in which AB = AC and D is a
point on AC such that BC2 = AC CD. Prove that
BD = BC.
3. Prove that area of an equilateral triangle described
on the side of a right angled isosceles triangle is half
the area of the equilateral triangle described on its
hypotenuse.
4. Prove that the equilateral triangles described on
the two sides of a right angled triangle are together
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