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P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square.

Given P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD... View Article

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle.

Given P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a... View Article

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

Given P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a... View Article

In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.

Given A parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E.... View Article

A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Given ΔABC with ∠A = 90o and ABC is an isosceles triangle, To Prove The vertex of the square opposite the vertex... View Article

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Given E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF To Prove... View Article

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Solution: According to given details ABCD is a rhombus. DE is the altitude on AB then AE = EB. From... View Article

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.

Solution: According to given details ABCD is parallelogram, DP ⊥ AB DQ ⊥ BC. ∠PDQ = 60o In quadrilateral DPBQ,... View Article

ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.

Solution: According to given details ABCD is a trapezium ∠A = ∠B = 45º We know that, angles opposite to... View Article

One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.

Solution: Let us assume the remaining three equal angles be x. We know that according to the quadrilateral angle sum property,... View Article

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Solution: All the four angles of a quadrilateral cannot be obtuse angles. Explanation We know that according to the quadrilateral... View Article

Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Solution: The given statement diagonals of a rectangle are equal and perpendicular is false. We know that, Diagonals of a... View Article

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Solution: According to the given details All the angles of a quadrilateral are equal. Let us the angles of the quadrilateral... View Article

In quadrilateral ABCD, ∠A + ∠D = 180º. What special name can be given to this quadrilateral?

Solution: According to the given details In quadrilateral ABCD, ∠A + ∠D = 180º From the property of trapezium we... View Article

Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?

Solution: The angles 110º, 80º, 70º and 95º cannot be the angles of a quadrilateral. Justification: By the quadrilateral angle... View Article

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Solution The given statement diagonals of a parallelogram are perpendicular to each other is false. Explanation Diagonals of a parallelogram... View Article

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.

Solution According to the given details OA = 3 cm OD = 2 cm We know that, diagonals of parallelogram bisect... View Article

If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a (A) rectangle (B) rhombus (C) parallelogram (D) quadrilateral whose opposite angles are supplementar

The correct answer is (D) quadrilateral whose opposite angles are supplementary Solution We know that, From angle sum property of... View Article

If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a (A) rhombus (B) parallelogram (C) trapezium (D) kite

The correct answer is (C) trapezium Solution As angle A, B, C and D of the quadrilateral ABCD, when taken... View Article

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if (A) PQRS is a rhombus (B) PQRS is a parallelogram (C) diagonals of PQRS are perpendicular (D) diagonals of PQRS are equal.

The correct answer is (D) diagonals of PQRS are equal. Solution We know that ABCD is a rhombus So AB... View Article

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