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Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10 PDF Download

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
(i) Statement of Basic Proportionality theorem.
(ii) 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

  • Cut an acute-angled triangle say ABC from a coloured paper.
  • Paste the ΔABC on ruled sheet such that the base of the triangle coincides with ruled line.
    Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10
  • Mark two points P and Q on AB and AC such that PQ || BC.Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10
  • Using a ruler measure the length of AP, PB, AQ and QC.
  • Repeat the same for right-angled triangle and obtuse-angled triangle.
  • Now complete the following observation table.

Observation
Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10

Result
In each set of triangles, we verified that AP/PB = AQ/QC

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

Activity Time
(i) Find x if DE | | BC.Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10

(ii) Is PQ | | AB?Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10
(iii) Find x if PQ | | BCLab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10

The document Lab Manual: Basic Proportionality Theorem for a Triangle | Lab Manuals for Class 10 is a part of the Class 10 Course Lab Manuals for Class 10.
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FAQs on Lab Manual: Basic Proportionality Theorem for a Triangle - Lab Manuals for Class 10

1. What is the Basic Proportionality Theorem for a Triangle?
Ans. The Basic Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
2. How can the Basic Proportionality Theorem be used to solve problems in triangles?
Ans. The Basic Proportionality Theorem can be used to solve problems related to similar triangles, where the sides are divided proportionally. By using the theorem, we can find the unknown lengths or ratios of sides in a triangle.
3. Can the Basic Proportionality Theorem only be applied to right triangles?
Ans. No, the Basic Proportionality Theorem can be applied to any type of triangle, not just right triangles. As long as the line is parallel to one side and intersects the other two sides, the theorem can be used.
4. Is there a formula to calculate the ratios of divided sides using the Basic Proportionality Theorem?
Ans. No, there is no specific formula to calculate the ratios of divided sides using the Basic Proportionality Theorem. Instead, the theorem provides a concept that allows us to set up proportions and solve for the unknown variables.
5. Can the Basic Proportionality Theorem be applied to polygons other than triangles?
Ans. No, the Basic Proportionality Theorem specifically applies to triangles. It states that the line parallel to one side of the triangle must intersect the other two sides. For polygons with more than three sides, different theorems and concepts are used.
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