**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.

You can also download **10Th NCERT Maths Solution** to help you to revise complete syllabus and score more marks in your examinations.

**Prerequisite Knowledge**

- Statement of Basic Proportionality theorem.
- 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.

- Mark two points P and Q on AB and AC such that PQ || BC.

- 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**

**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**

- Find x if DE | | BC.

- Is PQ | | AB ?

- 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:**

- Their corresponding angles are equal.
- 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) DC^{2} = CF x AC

(b) CF^{2} = DC x AC

(c) AC^{2} = 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**

- (a)
- (c)
- (a)
- (a)
- (d)
- (a)
- (a)
- (d)
- (a)
- (a)

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