Activity & Practical Pythagoras Theorem| Class 10th level | edugrown
- Pythagoras’ theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Aim
- To verify Pythagoras theorem by performing an activity.
Objective
- The area of the square constructed on the hypotenuse of a right-angled triangle is equal to the sum of the areas of squares constructed on the other two sides of a right-angled triangle.
MATERIALS REQUIRED
Coloured papers, pair of scissors, fevicol, geometry box, sketch pens, light coloured square sheet.
THEORY
- In a right-angled triangle the square of hypotenuse is equal to the sum of squares on the other two sides.
- Concept of a right-angled triangle.
- Area of square = (side)2
- Construction of perpendicular lines.
PROCEDURE
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- Take a coloured paper, draw and cut a right-angled triangle ACB right-angled at C, of sides 3 cm, 4 cm and 5 cm as shown in fig. (i).
- Paste this triangle on white sheet of paper.
- Draw squares on each side of the triangle on side AB, BC and AC and name them accordingly as shown in fig. (ii).
- Extend the sides FB and GA of the square ABFG which meets ED at P and CI at Q respectively, as shown in fig. (iii).
- Draw perpendicular RP on BP which meets CD at R. Mark the parts 1, 2, 3, 4 and 5 of the squares BCDE and ACIH and colour them with five different colours as shown in fig. (iv).
- Cut the pieces 1, 2, 3, 4 and 5 from the squares BCDE and ACIH and place the pieces on the square ABFG as shown in fig. (v).
- Take a coloured paper, draw and cut a right-angled triangle ACB right-angled at C, of sides 3 cm, 4 cm and 5 cm as shown in fig. (i).
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Observation
Cut pieces of squares ACIH and BCDH and completely cover the square ABFG.
∴ Area of square ACIH = AC2 = 9cm2
Area of square BCDE = BC2 = 16cm2
Area of square ABFG = AB2 = 25 cm2
∴ AB2 = BC2 + AC2
25 = 9 + 16
Result
Pythagoras theorem is verified.
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