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• Posted on July 21, 2026July 28, 2026

SEBA Class 10 Maths Chapter 6.2 Solutions: New Syllabus Triangles Guide

Searching for accurate SEBA Class 10 Maths Chapter 6.2 solutions? Exercise 6.2 is one of the most critical parts of the Class 10 Geometry syllabus. It focuses on the practical application of Theorem 6.1 (Basic Proportionality Theorem / Thales Theorem) and Theorem 6.2 (Converse of BPT).

Fully updated for the 2026-27 SEBA/ASSEB syllabus, this guide provides clear, step-by-step proofs for every question—from basic ratio calculations to advanced geometric proofs. Follow along below to master these concepts and boost your score in the upcoming HSLC board exams!

Core Concepts: Basic Proportionality Theorem & Converse

Theorem 6.1: Basic Proportionality Theorem (BPT / Thales 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.

Theorem 6.2: 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.

SEBA Class 10 Maths Chapter 6.2 Solutions (Step-by-Step)

Q. 2 E and F are points on the sides PQ and PR respectively of a Δ PQR. For each of the following cases, state whether EF || QR :

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

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

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

Q. 3 In Fig. 6.20, if LM || CB and LN || CD, prove that AM/AB = AN/AD.

Q. 4 In Fig. 6.21, DE || AC and DF || AE. Prove that BF/FE = BE/EC.

Q. 6 In Fig. 6.23, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Q. 7 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).

Q. 8 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).

Q.9 ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO.

Q. 10 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.

Q. 11 Assertion (A) : If in Δ ABC , D and E are two points on the sides AB and AC respectively such that DE || BC, then AD/AB = AE/AC.

Reason (R) : If a line is drawn parallel to one side of a triangle intersecting the two other sides, then it divides the two sides in the same ratio.

(A) Both (A) and (R) are true and (R) is the correct explanation of A

(B) Both (A) and (R) are true and R is not the correct explanation of A

(C) A is true but R is false

(D) A is false but R is true.

Q. 12

Q. 13 In a Δ ABC, D and E are two points on the sides AB and AC respectively such that DE || BC. If AD = x, AE = (x + 2), BD = (x – 2) and CE = (x – 1), the value of x is

(A) 2

(B) 3

(C) 4

(D) 5

💡 HSLC Exam Revision Tips

• Always Mention the Theorem: When solving numerical or proof problems in your exam, explicitly add “By Basic Proportionality Theorem (Theorem 6.1)” or “By Converse of BPT” next to your ratios to earn full step-marks.
• Draw Labeled Diagrams: Always re-draw the triangle on your answer sheet, clearly marking parallel lines like $DE \parallel BC$ before setting up your ratios.

❓ Frequently Asked Questions (FAQs)

Q1: What is the main difference between BPT (Theorem 6.1) and its Converse (Theorem 6.2)?

Ans: BPT states that if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio. The Converse states that if a line divides two sides in the same ratio, the line must be parallel to the third side.

Q2: Is the proof of Thales Theorem important for the SEBA HSLC exam?

Ans: Yes, proving Theorem 6.1 (Thales Theorem) directly is a frequently asked 4-mark or 5-mark question in SEBA/ASSEB board examinations.

🔗 Next Steps & Related Resources

• Previous Exercise: ⬅️ SEBA Class 10 Maths Chapter 6.1 Solutions (Similar Figures)
• Next Exercise: ➡️ SEBA Class 10 Maths Chapter 6.3 Solutions (Similarity Criteria)
• Complete Guide: 📂 SEBA Class 10 Maths All Chapters Solutions (New Syllabus)

Have a question about a specific proof in Exercise 6.2? Drop your query in the comment box below, and our team at ACIT will help you clear it up right away!