Basic Proportionality Theorem | Applications | Triangle Proportionality theorem Class 10
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.
Basic Proportionality Theorem
Applications of basic proportionality theorem
Triangle proportionality theorem
converse of basic proportionality 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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