Three angles of a quadrilateral measure 56°, 115° and 84°. Find the measure of the fourth angle.

The angles of a quadrilateral are in the ratio 2:4:5:7. Find the angles.

In the adjoining figure, is a trapezium in which If and find and

In the adjoining figure, is a square and ΔEDC is an equilateral triangle. Prove that

(i) AE = BE (ii) ∠DAE = 15°

In the adjoining figure, BM⊥AC and DN⊥AC. If BM = DN, prove that AC bisects BD.

In the given figure, is a quadrilateral in which and Prove that

(i) bisects and

(ii)

(iii)

In the given figure, ABCD is a square and If PB = QC = DR, prove that

(i) (ii)

(iii)

If is a point within a quadrilateral show that

In the adjoining figure, is a quadrilateral and is one of its diagonals. Prove that:

(i)

(ii)

(iii)

Prove that the sum of all the angles of a quadrilateral is 360°.

In the adjoining figure, is a parallelogram in which Calculate and

In the adjoining figure, is a parallelogram in which and Calculate and

In the adjoining figure, is a parallelogram in which If the bisectors of and meet at prove that

(i) (ii) and (iii)

In the adjoining figure, is a parallelogram in which and

Calculate (i) (ii) (iii) (iv)

In a||gm if and find the value of and the measure of each angle of the parallelogram.

If an angle of a parallelogram is four-fifths of its adjacent angle, find the angles of the parallelogram.

Find the measure of each angle of a parallelogram, if one of its angles is 30° less than twice the smallest angle.

is a parallelogram in which and its perimeter is 30 cm. Find the length of each side of the parallelogram.

In each of the figures given below, is a rhombus. Find the value of and in each case.

The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus.

In each of the figures given below, is a rectangle. Find the values of and in each case.

In the adjoining figures, is a square. A line segment cuts at and the diagonal at such that and Find the value of

In the adjoining figures, and are perpendiculars to the diagonal of a ||gm Prove that

(i) (ii)

In the adjoining figures, is a parallelogram in which the bisectors of and intersect at a point Prove that

In the adjoining figures, is a parallelogram. If and are points on and respectively such that and prove that is a parallelogram.

In the adjoining figures, is a parallelogram whose diagonals intersect each other at A line segment is drawn to meet at and at Prove that

In the adjoining figures, is a parallelogram in which is produced to so that Prove that bisects

In the adjoining figures, is a parallelogram and is the midpoint of side If and when produced meet at prove that

A is given. If lines are drawn through parallel respectively to the sides and forming as shown in the adjoining figure, show that

In the adjoining figure, is a triangle and through lines are drawn, parallel respectively to and intersecting at and Prove that the perimeter of is double the perimeter of

In the adjoining figure, is a trapezium in which and is the midpoint of A line segment meets at Show that is the midpoint of

In the adjoining figure, is a in which and are the midpoints of and respectively. If is a line segment that cuts and at and respectively, prove that

In the adjoining figure, is a trapezium in which and are the midpoints of and respectively. and when produced meet at Also, and intersect at Prove that (i) (ii) (iii)

In the adjoining figure, is a median of and Show that is also a median of

In the adjoining figure, and are the medians of and Show that

In the adjoining figure, is a parallelogram. is the midpoint of and through a line segment is drawn parallel to to meet produced at and it cuts at Prove that

(i) (ii)

Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.

In the adjoining figure, are the midpoints of the sides and respectively, of Show that and

Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.

Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rhombus is a rectangle.

Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a square is a square.

Prove that the line segments joining the midpoints of opposite sides of a quadrilateral bisect each other.

In the given figure, is a quadrilateral whose diagonals intersect at right angles. Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides is a rectangle.

Three angles of a quadrilateral are 80^o, 95^o and 112^o. Its fourth angle is

Three angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. The smallest of these angles is

In the given figure, ABCD is a parallelogram in which ∠BAD = 75° and ∠CBD = 60°. Then, ∠BDC = ?

In which of the following figures are the diagonals equal?

If the diagonals of a quadrilateral bisect each other at right angles, then the figure is a

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is

The length of each side of a rhombus is 10cm and one of its diagonals is of length 16 cm. The length of the other diagonal is

If ABCD is a parallelogram with two adjacent angles ∠A = ∠ B, then the parallelogram is a

In a quadrilateral ABCD, if AO and BO are the bisectors of ∠A and ∠B respectively, ∠C = 70° and ∠D = 30°. Then, ∠AOB = ?

The bisectors of any two adjacent angles of a parallelogram intersect at

The bisectors of the angles of a parallelogram enclose a

The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a

The figure formed by joining the mid-points of the adjacent sides of a square is a

The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a

The figure formed by joining the mid-points of the adjacent sides of a rectangle is a

The figure formed by joining the mid-points of the adjacent sides of a rhombus is a

If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

If one angle of a parallelogram is 24^o less than twice the smallest angle, then the largest angle of the parallelogram is

In the given figure, ABCD is a parallelogram in which ∠BDC = 45° and ∠BAD = 75°. Then, ∠CBD = ?

If area of a ||gm with sides a and b is A and that of a rectangle with sides a and b is B, then

In the given figure, ABCD is a ||gm and E is the mid-point of BC. Also, DE and AB when produced meet at F. Then,

The parallel sides of a trapezium are a and b respectively. The line joining the mid-points of its non-parallel sides will be

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

In the given figure, ABCD is a parallelogram, M is the mid-point of BD and BD bisects ∠B as well as ∠D. Then, ∠AMB = ?

In the given figure, ABCD is a rhombus. Then,

In a trapezium ABCD, if AB || CD, then (AC² + BD²) = ?

Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is

In the given figure, AD is a median of ΔABC and E is the mid-point of AD. If BE is joined and produced to meet AC in F, then AF = ?

If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6: 4, then ABCD is a

Which of the following is not true for a parallelogram?

If APB and CQD are two parallel lines, then the bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD enclose a

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that ∠DAC = 30° and ∠AOB = 70°. Then, ∠DBC = ?

Three statements are given below:

I. In a ||gm, the angle bisectors of two adjacent angles enclose a right angle.

II. The angle bisectors of a ||gm form a rectangle.

III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which is true?

Three statements are given below:

I. In a rectangle ABCD, the diagonal AC bisects ∠A as well as ∠C.

II. In a square ABCD, the diagonal AC bisects ∠A as well as ∠C.

III. In a rhombus ABCD, the diagonal AC bisects ∠A as well as ∠C.

Which is true?

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is quadrilateral ABCD a ||gm?

I. Diagonals AC and BD bisect each other.

II. Diagonals AC and BD are equal.

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is quadrilateral ABCD a rhombus?

I. Quad. ABCD is a ||gm.

II. Diagonals AC and BD are perpendicular to each other.

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is ||gm ABCD a square?

I. Diagonals of ||gm ABCD are equal.

II. Diagonals of ||gm ABCD intersect at right angles.

In each of the questions one question is followed by two statements I and II. Choose the correct option.

Is quad. ABCD a parallelogram?

I. Its opposite sides are equal.

II. Its opposite angles are equal.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Match the following columns:

The correct answer is:

(a) -……, (b) -……..,

(c) -……, (d) -………,

Match the following columns:

The correct answer is:

(a) -……, (b) -……..,

(c) -……, (d) -………,

Which is false?

If P is a point on the median AD of a ΔABC, then ar (ΔABP) = ar(ΔACP).

The angles of a quadrilateral are in the ratio 1:3:5:6. Find its greatest angle.

In a ΔABC, D and E are the mid-points of AB and AC respectively and DE = 5.6 cm. Find the length of BC.

In the given figure, AD is the median and DE || AB. Prove that BE is the median.

In the given figure, lines l, m and n are parallel lines and the lines p and q are transversals. If AB = 5 cm, BC = 15 cm, then DE : EF = ?

ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

The diagonals of a rectangle ABCD intersect at the point O. If ∠BOC = 50°, then ∠OAD = ?

Match the following column:

The correct answer is:

(a) -……, (b) -……..,

(c) -……, (d) -………,

The diagonals of a rhombus, ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ?

ABCD is a trapezium in which AB || CD and AD = BC, then ∠A = ∠B is

Look at the statements given below:

I. If AD, BE and CF be the altitudes of a ΔABC such that AD = BE = CF, then ΔABC is an equilateral triangle.

II. If D is the mid-point of hypotenuse AC of a right ΔABC, then BD = AC.

III. In an isosceles ΔABC in which AB = AC, the altitude AD bisects BC.

Which is true?

A. I only B. II only

C. I and III D. II and III

In the given figure, D and E are two points on side BC of ΔABC such that BD = DE = EC.

Prove that

ar (ΔABD) = ar (ΔADE) = ar (ΔAEC).

In the given figure ABCD, DCFE and ABFE are parallelograms. Show that ar(ΔADE) = ar(ΔBCF).

In the given figure, ABCD is a trapezium in which AB || DC and diagonals AC and BD intersect at O. Prove that ar(ΔAOD) = ar(ΔBOC).

Show that a diagonal divides a parallelogram into two triangles of equal area.

In the given figure, AC is a diagonal of quad. ABCD in which BL ⊥ AC and DM ⊥ AC. Prove that or (quad. ABCD)

||gm ABCD and rectangle ABEF have the same base AB and are equal in areas. Show that the perimeter of the ||gm is greater than that of the rectangle.

In the adjoining figure, ABCD is a ||gm and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.

In the adjoining figure, ABCD and PQRC are rectangles, where Q is the mid-point of AC.

Prove that (i) DP = PC (ii)