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Chapter Analysis
Intermediate16 pages • EnglishQuick Summary
Chapter 3 of Class 8 Mathematics, 'Understanding Quadrilaterals', unravels the features and properties of different types of quadrilaterals. It discusses various kinds of quadrilaterals like parallelograms, rectangles, rhombuses, squares, and kites, detailing their distinct characteristics. The chapter aims to nurture an understanding of basic geometric concepts through properties of the angles and sides, emphasizing the relationships between different quadrilaterals.
Key Topics
- •Properties of quadrilaterals
- •Different types of quadrilaterals
- •Properties and definitions of parallelograms, rectangles, rhombuses, squares, and kites
- •Angle sum property of quadrilaterals
- •Diagonals of quadrilaterals and their properties
Learning Objectives
- ✓Understand the different properties of quadrilaterals
- ✓Identify various types of quadrilaterals
- ✓Learn the properties related to the diagonals and sides of quadrilaterals
- ✓Solve problems related to angles and sides in quadrilaterals
- ✓Distinguish between regular and irregular quadrilaterals
Questions in Chapter
State whether True or False: (a) All rectangles are squares (b) All rhombuses are parallelograms (c) All squares are rhombuses and also rectangles (d) All squares are not parallelograms.
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Explain how a square is: (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle
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Name the quadrilaterals whose diagonals: (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal
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Explain why a rectangle is a convex quadrilateral.
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ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B, and C.
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Additional Practice Questions
How many sides does a regular polygon have if each of its exterior angles is 30°?
mediumAnswer: The exterior angle of a regular polygon is calculated with: 360° / n, where n is the number of sides. Solving 30 = 360 / n gives n = 12. Therefore, the polygon has 12 sides.
What happens to the diagonals of a kite?
easyAnswer: In a kite, the diagonals intersect at a right angle, and one of the diagonals bisects the other, thus the diagonals of a kite are perpendicular bisectors.
Explain why all rhombuses are also parallelograms.
easyAnswer: A rhombus, by definition, has all sides of equal length and opposite sides that are parallel, meeting the criterion of a parallelogram.
Is it possible for a trapezium to have its non-parallel sides of equal length? If yes, what is such a trapezium called?
mediumAnswer: Yes, a trapezium can have non-parallel sides of equal length and is termed an isosceles trapezium.
A rectangle has diagonals of 10 cm. Are these diagonals perpendicular?
mediumAnswer: No, in a rectangle, while the diagonals are of equal length and bisect each other, they are not typically perpendicular.
If a parallelogram's adjacent angles are given to be in the ratio 2:1, find each angle's measure.
mediumAnswer: Parallelogram's adjacent angles are supplementary. Let the angles be 2x and x; 2x + x = 180. Solving gives x = 60°, hence angles are 60° and 120°.
Why is a rectangle considered a special kind of parallelogram?
easyAnswer: A rectangle is a parallelogram with right angles, meaning it has all the properties of parallelograms plus the feature of equal angles.
Prove that the sum of interior angles of any quadrilateral is 360°.
mediumAnswer: A quadrilateral can be divided into two triangles; each triangle has angle sum of 180°, total 360°.
Determine the relationship between a square and a rhombus.
mediumAnswer: A square is a rhombus with all interior angles equal to 90°, meaning every square is a rhombus but not all rhombuses are squares.