Basic Proportionality Theorem for a Triangle

Basic Proportionality Theorem for a Triangle

Objective
To verify the basic proportionality theorem by using parallel lines board, triangle cut outs.

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.
2. Paste the ΔABC on ruled sheet such that the base of the triangle coincides with ruled line.
   
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

Result
In each set of triangles, we verified that 

Learning Outcome
In all the three triangles the Basic Proportionality theorem is verified.