What is Trapezium ?
A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.
Properties :
(i) All the properties of a trapezoid
(ii) Non-parallel sides are congruent.
(iii) Diagonals are congruent.
(iv) Base angles are congruent.
(v) Opposite angles are supplementary
Find the value of the variable in each isosceles trapezoid.
Problem 1 :
Solution :
By observing the figure,
WR = TS
5x^{º} = 60^{º}
x^{º }= 60^{º}/5
x^{º} = 12
Problem 2 :
Solution :
Non parallel sides will be congruent. So,
NO = ML
3x^{º} = 45^{º}
x^{º }= 45^{º}/3
x^{º} = 15
Problem 3 :
Solution :
By observing the figure,
DC = AB
(3x + 15)^{º} = 60^{º}
3x^{º} + 15^{º} = 60^{º}
3x^{º }= 60^{º} - 15^{º}
3x^{º} = 45^{º}
x = 45^{º}/3
x = 15^{º}
Problem 4 :
Solution :
By observing the figure,
TV = US
2x – 1 = x + 2
Comparing like terms.
2x – x = 2 + 1
x = 3
Problem 5 :
Solution :
In a isosceles trapezium, diagonals are equal,
SU = TR
x + 1 = 2x - 3
x – 2x = -3 - 1
-x = -4
x = 4
Problem 6 :
Solution :
By observing the figure, it is isosceles trapezium. In which diagonals will be equal.
QS = RP
x + 5 = 3x + 3
Comparing like terms.
x – 3x = 3 - 5
-2x = -2
Divide both sides by -2.
x = 1
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM