Activity & Practical on Ratio of Areas of Two Similar Triangles| 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 “The ratio of the areas of two similar triangles
Objective
- To verify “The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides” by performing an activity.
MATERIALS REQUIRED
Chart paper, construction box, coloured pens, a pair of scissors, fevicol.
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 white chart paper and cut a ∆ABC withAB=6cm,BC=6cm,CA=6cmMark five points P1,P2,P3,P4,P5 at a distance of 1 cm on side AC andQ1,Q2,Q3,Q4,Q5 at a distance of 1 cm on side AB. ( Image 1)
Join P1Q1,P2Q2,….P5Q52. Draw parallel line to AC from Q1, Q2…. and parallel line to AB from P1, P2,.( Image 2)
This ∆ ABC is divided into 36 similar and equal in area of triangles.Construct a ∆ PQRwith PQ= Half of ABPR=Half of ACQR=Half of BC on other chart paper3. Mark D1,D2 and E1,E2 on sides PQ and PR ( Image3)
4. Divide ∆ PQR into 9 similar and equal in areas triangles ( Image 4)
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Observation
Area of ∆ABC=Area of 36 smaller triangles
Area of ∆ PQR=Area of 9 smaller triangles
Result
It is Verified that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
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