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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 each other in... 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, the sum of... 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 angle sum... 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 rectangle bisect... 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 = x We know... 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 know... 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... 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 each other. Then, AC = 2AO... 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 in order that are in the ratio 3: 7: 6:... 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 = BC = CD = DA Now, Since D and C are... View Article

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

The correct answer is (C) diagonals of PQRS are perpendicular Solution Let the rectangle be ABCD, From the properties of the rectangle,... View Article

ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is (A) 40º (B) 45º (C) 50º (D) 60º

The correct answer is (C) 50º Solution According to the given details, ABCD is a rhombus ∠ACB = 40° ∵ ∠ACB = 40°... View Article

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is (A) 55º (B) 50º (C) 40º (D) 25º

The correct answer is (B) 50º Solution According to the given details A diagonal of a rectangle is inclined to one side of the rectangle at... View Article

Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is (A) 90º (B) 95º (C) 105º (D) 120º

The correct answer is (D) 120º Solution According to the given details Three angles of a quadrilateral are 75°, 90° and 75°... View Article

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

Given Δ ABC with median AD. To Prove AB + AC > 2AD AB + BC > 2AD BC + AC > 2AD Construction: Extend AD to E such that DE = AD... View Article

ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.

Given ABC is an isosceles triangle in which AC = BC. To Prove AE = BD Proof According to given details From Δ ADC and Δ... View Article

ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

Given Δ ABC and Δ DBC on the same base BC. Also, AB = AC and BD = DC. To Prove AD is the perpendicular bisector of BC i.e.,... View Article

O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that Δ OCD is an isosceles triangle.

Given A square ABCD and OA = OB = AB. To Prove Δ OCD is an isosceles triangle. Proof In square ABCD, We note that ∠1 and... View Article

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