ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD
Line segment joining the mid-points M and N of parallel sides AB and DC,
respectively of a trapezium ABCD is perpendicular to both the sides AB and DC.
Prove that AD = BC.
Two lines l and m intersect at the point O and P is a point on a line n passing
through the point O such that P is equidistant from l and m. Prove that n is the
bisector of the angle formed by l and m.
In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.
In a triangle ABC, D is the mid-point of side AC such that BD = 1/2 AC. Show that ∠ABC is a right angle.
Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.
ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.
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