Quadrilateral
ICSE Class 6 · Mathematics · Chapter 27
What this chapter covers
- Quadrilateral and its parts
- Interior and exterior of a quadrilateral
- Types of quadrilaterals
Key points
- A quadrilateral is a closed figure made of four straight line segments.
- It has four sides, four vertices and four angles.
- Adjacent sides meet at a vertex; opposite sides do not meet.
- A quadrilateral has four pairs of adjacent sides and two pairs of opposite sides.
- A diagonal joins two opposite vertices; every quadrilateral has two diagonals.
- The four sides divide the plane into the interior, the boundary and the exterior.
- A trapezium has only one pair of opposite sides parallel.
- A parallelogram has both pairs of opposite sides parallel, and its opposite sides are equal.
- A rectangle has four right angles and equal opposite sides.
- A square has four equal sides and four right angles.
- A rhombus has four equal sides, but its angles need not be right angles.
Questions answered
How many sides, vertices and angles does a quadrilateral have?
Four sides, four vertices and four angles.
In quadrilateral KLMN, name the side opposite to KL and the two sides adjacent to KL.
MN is opposite to KL. LM and NK are adjacent to KL.
Name the two diagonals of quadrilateral WXYZ.
WY and XZ.
Is AC a side or a diagonal of quadrilateral ABCD? Give a reason.
AC is a diagonal, because A and C are opposite vertices.
A point lies on side BC of quadrilateral ABCD. Is it in the interior, in the exterior, or on the boundary?
It is on the boundary.
A quadrilateral has only one pair of opposite sides parallel. What is it called?
A trapezium.
Draw a quadrilateral with all four sides 5 cm long and all four angles right angles. What is its most exact name, and how do you check your drawing?
It is a square. Draw it like the rectangle in the steps above, using 5 cm for every side. Then measure: each side should be 5 cm and each angle should be 90°.
Give one way in which a square and a rhombus are alike, and one way in which they differ.
Both have all four sides equal. A square has four right angles; a rhombus usually does not.