Class 8 Exam > Class 8 Notes > Mathematics Class 8- New NCERT (Ganita Prakash) > Points to Remember: Quadrilaterals
Points to Remember: Quadrilaterals | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download
| Table of contents |
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| Polygon |
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| Concave polygons |
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| Convex polygons |
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| Regular and irregular polygons |
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| Parallelogram |
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| Rhombus |
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| Rectangle |
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| Square |
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| Kite |
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| Trapezium |
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| Diagonal |
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Polygon
A simple closed curve made up of only line segments is called a polygon.
Concave polygons
Concave polygons are those polygons in which at least one interior angle is a reflex angle and it points inwards. They have a minimum of 4 sides
Convex polygons
A polygon is a two-dimensional shape that has a minimum of three sides and angles. A convex polygon is a shape in which all of its vertices point in the outward direction.
Regular and irregular polygons
A regular polygon is a two-dimensional shape having all sides of equal length and all interior angles of equal measure.
An irregular polygon, also known as non-regular polygon is a shape that does not have all sides of equal length and all angles of equal.
Parallelogram
A quadrilateral with each pair of opposite sides parallel.
- Opposite sides are equal.
- Opposite angles are equal.
- Diagonals bisect one another.
Rhombus
A parallelogram with sides of equal length.
- All the properties of a parallelogram.
- Diagonals are perpendicular to each other.
Rectangle
A parallelogram with a right angle.
- All the properties of a parallelogram.
- Each of the angles is a right angle.
- Diagonals are equal.
Square
- A rectangle with sides of equal length.
- All the properties of a parallelogram, rhombus, and a rectangle.
Kite
A quadrilateral with exactly two pairs of equal consecutive sides.
- The diagonals are perpendicular to one another.
- One of the diagonals bisects the other.
- From figure, m∠B=m∠D but m∠A≠m∠C
Trapezium
A quadrilateral having exactly one pair of parallel sides.
Diagonal
- A simple closed curve is made up of only line segments.
- A line segment connecting two non-consecutive vertices of a polygon is called diagonal.
Convex: The measure of each angle is less than 180º .
Concave: The measure of at least one angle is more than 180º.
Quadrilateral: A polygon having four sides.
Element of quadrilateral:
(i) Sides: Line segments joining the points.
(ii) Vertices: Point of intersection of two consecutive sides.
(iii) Opposite sides: Two sides of a quadrilateral having no common endpoint.
(iv) Opposite Angles: Two angles of a quadrilateral not having a common arm.
(v) Diagonals: A line segment is obtained by joining the opposite vertices.
(vi) Adjacent Angles: Two angles of a quadrilateral having a common arm.
(vii) Adjacent Sides: Two sides of a quadrilateral having a common endpoint.
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FAQs on Points to Remember: Quadrilaterals - Mathematics Class 8- New NCERT (Ganita Prakash)
| 1. What are the main characteristics that differentiate concave and convex polygons? |  |
Ans. Convex polygons are shapes where all interior angles are less than 180 degrees, and any line segment drawn between two points inside the polygon remains inside the polygon. In contrast, concave polygons have at least one interior angle greater than 180 degrees, meaning that there exists at least one line segment between two points that lies outside the polygon.
| 2. How can you classify quadrilaterals, and what are the key properties of a parallelogram? | |
Ans. Quadrilaterals can be classified into various types based on their properties, such as parallelograms, rectangles, rhombuses, squares, kites, and trapeziums. A parallelogram is a type of quadrilateral where opposite sides are parallel and equal in length, and opposite angles are equal. The diagonals of a parallelogram bisect each other at their midpoints.
| 3. What makes a shape a regular polygon, and can you provide examples of both regular and irregular polygons? | |
Ans. A regular polygon is defined as a polygon with all sides and angles equal. Examples of regular polygons include an equilateral triangle and a square. An irregular polygon, on the other hand, has sides and angles that are not all the same, such as a rectangle (which has equal angles but unequal sides) or a scalene triangle (which has all sides of different lengths).
| 4. What are the distinguishing features of a kite in geometry? | |
Ans. A kite is a type of quadrilateral that has two pairs of adjacent sides that are equal in length. The diagonals of a kite intersect at right angles, and one of the diagonals bisects the other. Additionally, the angles between the pairs of equal sides are equal, which is a key feature that differentiates a kite from other quadrilaterals.
| 5. How does a trapezium differ from other quadrilaterals, and what types of trapeziums exist? | |
Ans. A trapezium (or trapezoid in some regions) is a quadrilateral that has at least one pair of parallel sides. The sides that are not parallel are called the legs. There are two main types of trapeziums: isosceles trapeziums, where the legs are of equal length, and right trapeziums, which have one angle that is a right angle. This unique property of having parallel sides sets trapeziums apart from other quadrilaterals.
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