CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 33(a)
If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.
Answer
The converse is the 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; in , gives .
🔒 Step-by-step solution
Sign up free to see every step of how it is worked out.
From the board paper
More questions from Triangles
Class 10 Maths — every question with an expert-verified, step-by-step solution.
- Q1 Fill in the blanks using the correct word given in brackets: (i) All…
- Q2 Give two different examples of pair of: (i) similar figures (ii…
- Q3 State whether the following quadrilaterals are similar or not:
- Q1 In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii…
- Q2 E and F are points on the sides PQ and PR respectively of a triangle…
- Q3 In Fig. 6.18, if LM ∥ CB and LN ∥ CD, prove that AM/(AB)=AN/(AD).
- Q4 In Fig. 6.19, DE ∥ AC and DF ∥ AE. Prove that BF/(FE) = BE/(EC).
- Q5 In Fig. 6.20, DE ∥ OQ and DF ∥ OR. Show that EF ∥ QR.
- Q6 In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively…
- Q7 Using Theorem 6.1, prove that a line drawn through the mid-point of…
- Q8 Using Theorem 6.2, prove that the line joining the mid-points of an…
- Q9 ABCD is a trapezium in which AB ∥ DC and its diagonals intersect ea…
All 424 questions on Triangles → Browse all Maths chapters →