Question

Lab Manual - To verify the Basic Proportionality Theorem

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Answer 1

Hey!

BPT (Basic Proportionality Theorem) is also known as Thales Theorem.

-prefer attachment

So,

ar(BDE)=ar(DEC)

Therefore, from eq. (i),(ii) and (iii)

We have,

AD/DB = AE/EC

Hence Proved.

Answer 2

Answer:

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Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle, to intersect the other two sides at distinct points, the other two sides are divided in the same ratio.

Prerequisite Knowledge

1. Statement of Basic Proportionality theorem.
2. Drawing a line parallel to a given line which passes through a given point.

Materials Required

White chart paper, coloured papers, geometry box, sketch pens, fevicol, a pair of scissors, ruled paper sheet (or Parallel line board).

Procedure

1. Cut an acute-angled triangle say ABC from a coloured paper. [See the image]
2. Paste the ΔABC on ruled sheet such that the base of the triangle coincides with ruled line. [see the image]
3. Mark two points P and Q on AB and AC such that PQ || BC.
4. Using a ruler measure the length of AP, PB, AQ and QC.
5. Repeat the same for right-angled triangle and obtuse-angled triangle.
6. Now complete the following observation table.

Observation

[See the image]

Result

In each set of triangles, we verified that \frac { AP }{ PB } =\frac { AQ }{ QC }

Learning Outcome

Students will observe that in all the three triangles the Basic Proportionality theorem is verified.

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