Quadrilaterals ...

Which of the following quadrilaterals is formed by joining the mid-points of the consecutive sides of a quadrilateral?

Which of the following quadrilateral has no pair of parallel sides?

The opposite angles of a quadrilateral are equal and the adjacent angles are in ratio 1 : 3. What will be the measure of all the angles in ascending order?

In the given figure, LMPN is a trapezium with LM || NP, MPO = 30° and MO ⊥ NP. What is the measure of LNO if LMP = 2LNO?

In the given figure, ABCD is a rectangle in which ∠OAB = y°, ∠OBC = x° and ∠COD = 110°, find the values of x and y, respectively.

If two consecutive angles of a parallelogram are (x + 80)° and (5x + 40)°, what is the name of the quadrilateral?

In a quadrilateral ABCD, if ∠A = 90° and ∠B : ∠C : ∠D = 3 : 4 : 8, then what will be the measures of the other angles?

A rhombus is made inside a circle. One diagonal BD of the rhombus passes through the centre of the circle. If ∠ACB = 50°, find∠ADB.

In the given quadrilateral, what is the sum of A and C?

If a quadrilateral has equal diagonals but unequal and non-parallel adjacent sides, then which of the following quadrilaterals can it be?

Find the largest angle of a parallelogram, if one angle of a parallelogram is 4° less than one-third of its adjacent angle.

Consider the following information to identify the shape(s).

(1) The quadrilateral has two pairs of opposite sides parallel.
(2) The diagonals bisect the angles and are perpendicular bisectors of each other.
(3) Consecutive angles are supplementary but not equal.

A parallelogram PQRS is inscribed in a circle. PR and QS are chords of the circle that intersect at point O. Find SQP.

In a rectangle MNOP, Q, R, S, and T are the mid-points of MN, NO, OP and PM, respectively. The perimeter of the rectangle is 32 cm and the area is 60 cm². Find the length of TQ, given the largest side is MN.

In a parallelogram ABCD, DE is the angle bisector of ADC, EG is produced such that EDG = EGD and EF is the bisector of DEG. If EG ∥ BC, and points F and G are on line DC, then

In the following figure, PQRS is a quadrilateral, SR is produced to N and PQ is produced to M such that QMNR is a parallelogram. C and D are the mid-points of QM and RN, respectively. Also, SC and PD intersect at O and bisects RQ. If OD = OC, then which of the following options is correct?

In the given rectangle ABDC, AE is the bisector of CAB and AE ∥ HI. If GFD = 48°, then GJH equals

In the following figure, X is the mid-point of PH. What would be the shape of figure XUZH, if PUIH is a parallelogram and Z is the mid-point of IU?

In the given figure, if PQ || NO and QR || FG, find the value of QF.

In the given figure, PQRS is a square, and M and N are the points on SR and RQ, respectively. What is the ratio of the length of MN to that of SQ, if MN is 6 cm shorter than SQ?

Read the statements carefully and find out the option that holds.

Statement 1: Opposite angles of a rhombus have equal measure.
Statement 2: Arhombus is an ortho-diagonalquadrilateral. Its diagonals bisectopposite angles.

Read the statements carefully and mark them as true (T) or false (F).

1. Every rhombus is a parallelogram.
2. Two pairs of equal-length sides that are adjacent to each other is a kite.
3. Rhombus with one angle as 90° is a square.
4. Every parallelogram is a rectangle in which two opposite sides are equal.

Fill in the blanks:

1. The opposite sides of a _______ are parallel and equal.
2. If each angle measures 90° and diagonals are not perpendicular bisectors of each other, then it is a __________.
3. A parallelogram cannot be a _______.

In the given rectangle ABCD, FEG is a triangle and DF = GC = . The perimeter of rectangle ABCD is 56 cm and that of rectangle IHCD is 42 cm. If J and K are the respective mid-points of EF and EG, find the area of the trapezium FJKG given that the length and width of the rectangle ABCD are in the ratio 4 : 3.

Match the columns: