Practical Geometry - Maths Class 8th - Ex 4.5 - Q1 - Chapter 4 - NCERT - CBSE

Описание: Practical Geometry - Maths Class 8th - Ex 4.5 - Question 1 - Chapter 4 - NCERT - CBSE

Full exercise on Practical Geometry, fully solved. This is a video tutorial for 8th class NCERT CBSE students. For other educational stuff, subscribe and press bell icon.

You have learnt how to draw triangles in Class VII. We require three measurements (of sides and angles) to draw a unique triangle. Since three measurements were enough to draw a triangle, a natural question arises whether four measurements would be sufficient to draw a unique four sided closed figure, namely, a quadrilateral.

Constructing a Quadrilateral

How to construct/draw 60 degrees angle with compasses only
How to construct/draw 90 degrees angle with compasses only
How to construct/draw 105 degrees angle with compasses only
How to construct/draw 85 degrees angle with compasses only
How to construct/draw 110 degrees angle with compasses only
How to construct/draw 60 degrees angle without protractor
How to construct/draw 90 degrees angle without protractor
How to construct/draw 105 degrees angle without protractor
How to construct/draw 85 degrees angle without protractor
How to construct/draw 110 degrees angle without protractor

Some Special Cases
To draw a quadrilateral, we used 5 measurements in our work. Is there any quadrilateral which can be drawn with less number of available measurements? The following examples examine such special cases.

Example 5: Draw a square of side 4.5 cm.
Solution: Initially it appears that only one measurement has been given.Actually we have many more details with us, because the figure is a special quadrilateral, namely a square. We now know that each of its angles is a right angle.

Example 6: Is it possible to construct a rhombus ABCD where AC = 6 cm and BD = 7 cm? Justify your answer.
Solution: Only two (diagonal) measurements of the rhombus are given. However, since it is a rhombus, we can find more help from its properties. The diagonals of a rhombus are perpendicular bisectors of one another.

EXERCISE 4.5
Draw the following.
1. The square READ with RE = 5.1 cm.
2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
4. Aparallelogram OKAY where OK = 5.5 cm and KA= 4.2 cm.

WHAT HAVE WE DISCUSSED?
1. Five measurements can determine a quadrilateral uniquely.
2. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.
3. A quadrilateral can be constructed uniquely if its two diagonals and three sides are known.
4. A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are known.
5. A quadrilateral can be constructed uniquely if its three sides and two included angles are given.

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