#### In a square ABCD, the diagonals bisect each other at O. If AO = 3 cm, then the length of BD is ____.

AC = 2 × AO = 2 × 3 = 6 cm BD = AC = 6 cm (∵ Diagonals of a square are equal)

#### A quadrilateral is a trapezium, if ____.

A quadrilateral is a trapezium, if one pair of its opposite sides are parallel.

#### In a quadrilateral, if the opposite sides are equal and the diagonals are also equal, then the quadrilateral is a ____.

In a quadrilateral, if the opposite sides are equal and the diagonals are also equal, then the quadrilateral is a rectangle.

#### If sum of two angles of a quadrilateral is 200°, then the sum of the remaining two angles is 160°.

Given statement is a true statement as sum of the four angles of a quadrilateral is 360°.

#### A parallelogram is a rhombus, if ____.

Diagonals of rhombus are not equal and intersect each other at right angles.

#### No quadrilateral exists with its angles in the ratio 1: 2: 3: 6.

If the angles are in the ratio 1 : 2 : 3 : 6, the angles will be 30°, 60°, 90° and 180°. But no angle of a quadrilateral can be 180°.

#### If quadrilateral ABCD is a parallelogram, then the sum of ∠C and ∠D is ____.

∠C and ∠D are corresponding interior angles ∴ ∠C +∠D = 1800

#### The line segment joining the mid-points of two sides of triangle is parallel to the third side.

The line segment joining the mid-points of two sides of triangle is parallel to the third side.

#### In a rectangle the length of one diagonal is 15 cm and the other diagonal measures 3x + 3. The value of x is ____.

Diagonals of a rectangle are equal ⇒ 3x + 3 = 15 ⇒ 3x = 12 ∴ x = 4