NCERT Class 10 Maths Lab Manual – Basic Proportionality Theorem for a Triangle

NCERT Class 10 Maths Lab Manual – 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.

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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 \(\frac { AP }{ PB } =\frac { AQ }{ QC }\)

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

Activity Time

1. Find x if DE | | BC.
   
2. Is PQ | | AB ?
   
3. Find x if PQ | | BC
   

Viva Voce

Question 1.
Is there any other name for B.P.T. (Basic Proportionality Theorem) ?
Answer:
Yes, Thales Theorem

Question 2.
Name the mathematician who gave B.P.T.
Answer:
Greek mathematician Thales

Question 3.
What is the statement of B.P.T. ?
Answer:
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.

Question 4.
Can we prove Mid-point theorem by using B.P.T. ?
Answer:
Yes

Question 5.
Is the B.P.T. applicable for a scalene triangle ?
Answer:
Yes

Question 6.
What is the converse of B.P.T. ?
Answer:
If a line divides any two sides of a triangle in the same ratio, the line is parallel to the third side of the triangle.

Question 7.
Give two different examples of pairs of similar figures.
Answer:
Pair of squares, pair of circles

Question 8.
What are the conditions for two polygons of same number of sides to be similar ?
Answer:

1. Their corresponding angles are equal.
2. Their corresponding sides are proportional.

Multiple Choice Questions

Question 1.
In ∆ABC, if DE || BC,AD = 3.2, DB = 1.6, AE = x and EC = 2.1, then x is
(a) 4.2
(b) 3.2
(c) 1.6
(d) 4.8

Question 2.
In the given fig., LM || QR. Find LQ

(a) 3.1 cm
(b) 2.5 cm
(c) 3 cm
(d) None of these

Question 3.
In the given fig., DE || BC. If \(\frac { AE }{ AC } =\frac { 2 }{ 5 } \) and AB = 15 cm ,find AD.

(a) 6 cm
(b) 5 cm
(c) 4 cm
(d) 7 cm

Question 4.
What value of p will make ST || QR in the given fig.?

(a) 2
(b) 3
(c) 5
(d) None of these

Question 5.
Find x, if DC || AB.

(a) 7
(b) 3
(c) 5
(d) None of these

Question 6.
In the given fig., AB || DE and BD || EF. Find the correct relation.

(a) DC² = CF x AC
(b) CF² = DC x AC
(c) AC² = DC x CF
(d) None of these

Question 7.
If LM || CB and LN || CD, then choose the correct answer

(a) \(\frac { AM }{ AB } =\frac { AN }{ AD } \)
(b) \(\frac { AM }{ AB } =\frac { AD }{ AN } \)
(c) \(\frac { AB }{ AM } =\frac { AN }{ AD } \)
(d) \(\frac { AM }{ AB } \neq \frac { AN }{ AD } \)

Question 8.
In the given figure, DE || OQ and DF || OR, then which is the correct relation ?

(a) EF = \(\frac { 1 }{ 2 } \) QR
(b) EF ≠ QR
(c) EF = QR
(d) EF||QR

Question 9.
In the given figure DE || BC, then EC is

(a) 2 cm
(b) 1.5 cm
(c) 1 cm
(d) 3 cm

Question 10.
In the given figure ABC and AMP are two right triangles, right angled at B and M respectively. Then tick the correct answer.

(a) \(\frac { CA }{ PA } =\frac { BC }{ MP }\)
(b) \(\frac { CA }{ PA } \neq \frac { BC }{ MP }\)
(c) \(\frac { CA }{ PA } =\frac { MP }{ BC }\)
(d) \(\frac { CA }{ PA } \neq \frac { MP }{ BC }\)

Answers

1. (a)
2. (c)
3. (a)
4. (a)
5. (d)
6. (a)
7. (a)
8. (d)
9. (a)
10. (a)

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