what is the difference between an isosceles trapezium and a trapezium
Answers
Answer:
isosceles trapezium has two equal sides normal trapezium does not.
Answer:
Trapezium.
Its properties are:
(a) Opposite sides are parallel.
(b) Two pairs of adjacent angles add up to 180 degrees.
(c) The two non-parallel sides are unequal.
(d) The diagonals intersect.
(e) 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.
(f) A trapezium can be inscribed in a circle
(g) The sum of the four exterior angles is 4 right angles.
(h) The sum of the four interior angles is 4 right angles.
Isosceles trapezium.
Its properties are:
(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.
(k) If the sum of the equal sides and the shorter parallel side is more than the longer parallel side, the circumcentre will lie outside the isosceles trapezium and be on the line joining the midpoints of the parallel sides.
(l) If the sum of the equal sides and the shorter parallel side is equal to the longer parallel side, the circumcentre will be the midpoint of the longer parallel side.
(m) If the sum of the equal sides and the shorter parallel side is more than the longer parallel side, the circumcentre will lie inside the isosceles trapezium and be on the line joining the midpoints of the parallel sides.