Activity 1 Square Root Spiral Class 9 th

Activity -1 Square Root Spiral Class 9 th Prepared & Presented By Mrs. Pramila Kumari Sahoo TGT, Mathematics JNV, Jagatsinghpur, Odisha

Objective To construct a Square Root Spiral

Materials Required • Adhesive (Gum) • Geometry box • Marker • A piece of Drawing Sheet

Prerequisite Knowledge 1. Concept of number line: A number line is an imaginary line whose each point represents a real number.

3. Pythagoras Theorem: Perpendicular According to Pythagoras theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides containing right angle. In a triangle ABC, right angled at B. A Hy po ten us e B Base C

PROCEDURE 1. Take a piece of drawing sheet. 2. Draw a line segment PQ of length 1 unit. Refer the figure below P 1 Unit Q

3. Construct a line QX perpendicular to the line segment PQ, by using compass or a set square. X Refer the figure below P Q

4. From Q, draw an arc of 1 unit, which cut QX at C (say). X 5. Join PC. 1 Unit C P 1 Unit Q

Y D 1 X Un it C 1 Unit 6. Taking PC as base, draw a perpendicular CY to PC, by using compass or a set square. 7. From C, draw an arc of 1 unit, which cut CY at D (say). 8. Join PD. P 1 Unit Q

Y 1 Unit D X 1 Un it C 1 Unit 9. Taking PD as base, draw a E perpendicular Z DZ to PD, by using compass or a set square. 10. From D, draw an arc of 1 unit, which cut DZ at E (say) 11. Join PE. P 1 Unit Q

12. Keep repeating the above process for sufficient number of times. Then, the figure so obtained is called a ‘Square Root Spiral’. Z 1 U D 1 X Un it C 1 Unit t G 1 U K L nit Y 1 Unit F E H M P 1 Unit Q

Demonstration • Z 1 it Un Y 1 Unit X D 1 Un it C nit F 1 Unit 1 U K t G L 1 Uni In figure, ΔPQC is a right angled triangle. So, from Pythagoras theorem, E H M P 1 Unit Q

Z nit Y 1 Unit 1 U D X 1 Un it C nit F E 1 Unit 1 U K L 1 Uni t G H • M P 1 Unit Q

Z 1 Uni t D X 1 Un it C 1 Unit G H 1 Unit 1 U K L nit U 1 Y nit F E P 1 Unit Q Similarly, we will have M In right angled triangle PDE, PE= √ 4 In right angled triangle PEF, PF=√ 5 In right angled triangle PFG, PG = √ 6 In right angled triangle PGH, PH = √ 7 and so on.

Result A Square Root Spiral has been constructed.

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