# FIND MISSING VALUES INVOLVING ISOSCELES TRAPEZOID

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

5xº = 60º

xº = 60º/5

xº = 12

Problem 2 :

Solution :

Non parallel sides will be congruent. So,

NO = ML

3xº = 45º

xº = 45º/3

xº = 15

Problem 3 :

Solution :

By observing the figure,

DC = AB

(3x + 15)º = 60º

3xº + 15º = 60º

3xº = 60º - 15º

3xº = 45º

x = 45º/3

x = 15º

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

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