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.

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
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 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)
(b)
(c)
(d)

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

(a) EF = 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)
(b)
(c)
(d)

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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