Question

properties of a trapezium​

Answer 1

Answer:

PROPERTIES OF TRAPEZIUM ARE :

Step-by-step explanation:  

(a) One pair of 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.

(i) One pair of adjacent angles can each be a right angle. The other pair of adjacent angles will be supplementary angles but not 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) Rotate the isosceles trapezium about the shorter of the parallel sides as the axis of revolution. At both ends you get concave cones whose slant height is the non-parallel sides of the isosceles trapezium.

(l) Rotate the isosceles trapezium about the longer of the parallel sides as the axis of revolution. At both ends you get convex cones whose slant height is the non-parallel sides of the isosceles trapezium.

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Answer 2

Answer:

• A trapezium has the following properties: Like other quadrilaterals, the sum of all the four angles of the trapezium is equal to 360° A trapezium has two parallel sides and two non-parallel sides. The diagonals of regular trapezium bisect each other.
• The properties of the isosceles trapezoid are as follows:
• The properties of the isosceles trapezoid are as follows:The properties of trapezoid apply by definition (parallel bases).
• The properties of the isosceles trapezoid are as follows:The properties of trapezoid apply by definition (parallel bases).The legs are congruent by definition.
• The properties of the isosceles trapezoid are as follows:The properties of trapezoid apply by definition (parallel bases).The legs are congruent by definition.The lower base angles are congruent.
• The properties of the isosceles trapezoid are as follows:The properties of trapezoid apply by definition (parallel bases).The legs are congruent by definition.The lower base angles are congruent.The upper base angles are congruent.
• The properties of the isosceles trapezoid are as follows:The properties of trapezoid apply by definition (parallel bases).The legs are congruent by definition.The lower base angles are congruent.The upper base angles are congruent.Any lower base angle is supplementary to any upper base angle.

Step-by-step explanation:

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