Basic Proportionality Theorem | Applications | Triangle Proportionality theorem Class 10

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Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Converse of Basic Proportionality Theorem

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

00:02 Q1. In Fig. 6.17, (i) and (ii), DE || BC. Find EC in 00:25 (i) and AD in 02:17 (ii).

00:38 Basic Proportionality Theorem:If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

02:25 Apply Basic Proportionality Theorem.

04:00 Q10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.

04:30 Construction to solve.

06:34 triangle proportionality theorem

09:20 Q2. E and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases,state whether EF||QR :

09:47 (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

11:00 Basic Proportionality Theorem.

12:55 (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

14:04 Check BPT (Basic Proportionality Theorem) holds for different sides.

16:10 (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

17:11 Apply triangle proportionality theorem.

21:56 3. In Fig. 6.18, if LM || CB and LN || CD, prove that AM/AB = AN/AD .

22:45 Consider triangles and apply Basic Proportionality Theorem

25:47 Use Side-Splitter Theorem

27:31 Q4. In Fig. 6.19, DE || AC and DF || AE. Prove that BF/FE = BE/EC.

29:01 Triangle proportionality theorem

30:24 Q5. In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

32:01 Basic proportionality theorem

33:37 Q6. In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

35:20 Use triangle proportionality theorem

36:48 Q7. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

38:20 Use Basic proportionality theorem.

39:27 Q8. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

40:03 Converse of Basic proportionality theorem.

41:42 Q9. ABCD is a trapezium in which AB || DC and itsdiagonals intersect each other at the point O. Show that AO/BO = CO/DO.

learncbse.in

Basic Proportionality Theorem

Applications of basic proportionality theorem

Triangle proportionality theorem

proportionality theorem

converse of basic proportionality theorem

Side-Splitter Theorem

CBSE class 10 maths chapter 6 Triangles

CBSE class 10 maths NCERT Solutions chapter 6 Triangles

Solutions for CBSE class 10 Maths Chapter 6

NCERT solutions for class 10 maths Triangles

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