ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD
Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 2/3 of a right angle
AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater.
ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.
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.
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