Trapezium

Q.

$\mathrm{ABCD}$is a trapezium in which $AB\mathit{}II\mathit{}CD$. If $\angle \mathrm{ADC}$ is equal to twice $\angle \mathrm{ABC}$, $\mathrm{AD}=\mathrm{a}\mathrm{cm}$ and $\mathrm{CD}=\mathrm{b}\mathrm{cm}$, then find the length of $\mathrm{AB}$.

Q. If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 8 : 7 : 6 : 9, then PQRS is always a

1. Kite
2. Trapezium
3. Rhombus
4. Parallelogram

Q. The measure of the angles of a quadrilateral ABCD are respectively in the ratio 1 : 2 : 3 : 4. What type of quadrilateral is ABCD?

1. Trapezium
2. Square
3. Rectangle
4. Parallelogram

Q. Which of the following is not a parallelogram?

1. Square
2. Rectangle
3. Rhombus
4. Trapezium

Q.

In the figure ABCD is a trapezium. Find the values of $x$ and $y$.

Q.

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Q.

In the figure, PQRS in an isosceles trapezium. Find x and y.

Q.

The parallel sides of a trapezium are ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ respectively. The line joining the midpoints of its nonparallel sides will be

(a) $\frac{1}{2}(a-b)$

(b) $\frac{1}{2}(a+b)$

(c) $\frac{2ab}{(a+b)}$

(d) $\sqrt{ab}$

Q. Question 24
Which of the following is an equiangular and equilateral polygon?
a) Square
b) Rectangle
c) Rhombus
d) Right angled Triangle

Q. Question 1
One angle of a quadrilateral is of ${108}^{\circ }$ and the remaining three angles are equal. Find each of the three equal angles. Thinking Process:
The sum of all the angles in a quadrilateral is ${360}^{\circ }$, use this result and simplify it.

Q.

E is the mid-point of the side AD of the trapezium ABCD with AB ∥ DC. A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-point of BC.

Q. What is a quadrilateral with only one pair of opposite sides equal called?

1. Rhombus
2. Isosceless trapezium
3. Rectangle
4. Square

Q.

Is every rectangle a square?

Q.

In a trapezium ABCD, E and F be the midpoints of the diagonals AC and BD respectively. Then, EF = ?

(a) $\frac{1}{2}AB$

(b) $\frac{1}{2}CD$

(c) $\frac{1}{2}(AB+CD)$

(d) $\frac{1}{2}(AB-CD)$

Q. Which of the following is true about a trapezium?

1. It has two pairs of opposite sides parallel to each other
2. All the angles are equal
3. It has one pair of opposite sides parallel to each other.
4. All the sides are equal

Q.

In the adjoining figure, ABCD is a trapezium in which AB II DC. If $\angle A={55}^{\circ }and\angle B={70}^{\circ }$, find $\angle C\angle D$.

Q. The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Show that the quadrilateral is a trapezium.

Q. A line EF parallel to the base, divides the trapezoid into two trapezoids of equal perimeters. Calculate the ratio in which each of the non-parallel sides is divided.

Q.

A trapezium is a parallelogram.

1. True

2. False

Q. In the given figure, ABCD is a trapezium. M and N are mid points of diagonals AC and BD respectively. Which of the following is true?

1. MN || AB || CD
2. DN = 2 BN
3. DC = 2 EB
4. NE = 0.5 CN

Q. Sum of opposite angles of an isosceles trapezium is

1. ${90}^0$
2. ${150}^0$
3. ${120}^0$
4. ${180}^0$

Q. In the diagram, ABD and BCD are isosceles triangles, where $AB=BC=BD$. What type of a quadrilateral is ABCD?

1. Parallelogram
2. Kite
3. Rectangle
4. Trapezium

Q.

In the given figure, ABCD is a trapezium. M and N are midpoints of diagonals AC and BD respectively. Which of the following is true?

1. DC = 2 EB

2. MN || AB || CD

3. NE = 0.5 CN

4. DN = 2 BN

Q. ABCD is a trapezium with AB || CD. Find the value of $\angle$BAD (in degrees) if $\angle ADC={60}^o$.

1. 120

Q. Question 12 (ii)
ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that $\angle C=\angle D$.

Q. A field is in the form of an isosceles trapezium whose perimeter is 215 m. One of its non - parallel side is 50 m . What is the sum of its parallel sides?

Q.

Square is a special type of ____________.

Q.

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Then, AC = BD.

1. True

2. False

Q. In the trapezium ABCD shown below, if $\angle ADC={120}^{\circ }$, then find the measure (in degrees) of $\angle DCB$.

1. 60

Q. All parallelograms are trapeziums.

1. True
2. False