CBSE Class 10 Maths (Standard) 2025 · Paper 30/5/1 · Question 33
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points then it divides the two sides in the same ratio. Prove it. Also, state the converse of the above statement.
Answer
Hence proved: if a line parallel to meets at and at , then . Converse: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
🔒 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 →