# Properties of Isosceles Trapezium???

An **isosceles trapezium** has the following properties:

(a) Two pairs of adjacent angles add up to 180 degrees.

(b) When the two non-parallel sides are equal and two pairs of adjacent angles are equal it is called an isosceles trapezium.

(c) An isosceles trapezium can be inscribed in a circle.

(d) The diagonals of an isosceles trapezium are equal.

(e) The diagonals of an isosceles trapezium form a pair of congruent triangles with the equal sides as the base and the other pair - similar triangles.

(f) The two non-parallel sides are equal.

(g) The line joining the mid points of the non-parallel sides is parallel to the parallel sides and is equal to half the sum of the parallel sides.

(h) The sum of the four exterior angles is 4 right angles.

(i) The sum of the four interior angles is 4 right angles.

(j) By rotating an isosceles trapezium about the vertical axis joining the midpoints of the parallel sides, we get a frustum of a cone.

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