Lab Manual: Pythagoras Theorem | Lab Manuals for Class 10 PDF Download

Objective

Prerequisite Knowledge

• 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.

Materials Required
Coloured papers, pair of scissors, fevicol, geometry box, sketch pens, light coloured square sheet.

Procedure

• 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.
  
• 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.
  
• Extend the sides FB and GA of the square ABFG which meets ED at P and CI at Q respectively, as shown.
  
• 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.
  
• 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.
  

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.

Learning Outcome
Students will learn practically that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Activity Time

•  The area of an equilateral triangle described on the hypotenuse of a right-angled triangle is equal to the sum of the areas of equilateral triangles described on the other two sides.
  In ∆ACD, AC = DC = DA = 5cm
  ar(∆ACD) =
  In ∆ABE, AB = BE = EA = 3cm
  ar(∆ABE) =
  In ∆BCF, BC = CF = FB = 4cm
  ar(∆BCF) = Now, ar(∆ABE) + ar(∆BCF) =
  
  ∴ ar(∆ABE) + ar(∆BCF) = ar(∆ACD) verified.
• The area of a semi-circle described on the hypotenuse of a right-angled triangle is equal to the sum of the areas of semicircles described on the other two sides of right-angled triangle.