# To Study

Topics: Congruence, Triangle, Hypotenuse Pages: 5 (444 words) Published: May 12, 2013
Geometry in Real Life

To become familiar with the fact that geometry (similar triangles) can be Description

In this project I tried to find situations in daily life where geometrical notions can be effectively used, I selected the following examples: 2. To find height of a tower 1. To find the width of a river

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used in real life to find height of certain things and width of many others.

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Objective

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To find the width of a river
Walked along the river, fixed another pole at R at a distance of 9 metres. Walked another 3 metres to S, from here walked at right angles to the river till the point T is reached such that T is directly in line with R and P. width of the river was determined. Measured the distance ST. Using the property of similarity of triangles the

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Fixed a pole at Q directly opposite to a tree P on the other side of the river.

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In right triangle RQP and RST Angle PRQ = angle TRS (vertically opposite angles)   ൌ    ͻ ൌ  ͵ ୕୔ ୗ୘

Therefore triangle RQP ~ triangle RST by AA corollary

ଷ ଵ

------- (i)

Now ST = 4m, substituting its value in (i)  ͵ ൌ Ͷ ͳ

Therefore width of river = 12m

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QP = 12m

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Angle PQR = angle RST = 90°

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To find the height of a tower
shadow is at the same place as the ends of the shadow of the tower. Knowing the relevant distance, the height of the tower can be estimated.

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Placed the ruler upright in the shadow of the tower, so that the ends of its

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Solution :
In ∆ABE and ∆CDE angle E = angle E (common) angle B = angle D = 90°

by AA corollary
୅୆ େୈ

=

ୈ୉ ଶ଴଴ ଶହ

୆୉

஺஻ ஼஽

=

………

(i)

On measuring CD we get CD = 40cm Substituting value of CD in (i) ‫ܤܣ‬ ൌ൐  ͶͲ ଶ଴଴ ଶହ

=

= 320cm = 3.2m

‫׵‬Height of tower = 3.2m

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ൌ൐ AB =

ଶ଴଴ൈସ଴ ଶହ

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(Corresponding parts of similar triangles)

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‫∆׵‬ABE ~ ∆CDE

Conclusion
Thus we find that the geometry plays a very important role in our day to day life. Many examples involving different geometrical properties of triangles to measure for example:and circles could be examined. We can do lot of things which are impossible Measuring height of tree, height of building etc.

of similar triangles learnt in the classroom are useful.

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In particular, in the given project we discover situations in which properties

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