Class 10 Maths Chapter 6 Triangles | Exercise 6.2 & 6.3 Full Explanation & Solutions

Welcome to this comprehensive one-shot session on Class 10 Maths Chapter 6: Triangles (Exercise 6.2 & Exercise 6.3)! In this video, we cover complete step-by-step NCERT solutions and in-depth conceptual clarity for the Basic Proportionality Theorem (Thales Theorem), its converse, and all criteria for similarity of triangles (AAA, SAS, SSS). Whether you are preparing for your CBSE board exams or state board exams, this detailed lecture will help you master every theorem and problem with ease. ⏱️ Timestamps & Chapter Breakdown: [00:00] - Introduction to Triangles, BPT & Similarity Criteria (AAA, SAS, SSS) [03:56] - Ex 6.2 Q1: In Fig. 6.17 (i) & (ii), DE \parallel BC. Find EC in (i) and AD in (ii) [07:48] - Ex 6.2 Q2: E and F are points on sides PQ and PR of \Delta PQR. State whether EF \parallel QR [13:14] - Ex 6.2 Q3: In Fig. 6.18, if LM \parallel CB and LN \parallel CD, prove that \frac{AM}{AB} = \frac{AN}{AD} [15:29] - Ex 6.2 Q4: In Fig. 6.19, DE \parallel AC and DF \parallel AE. Prove that \frac{BF}{FE} = \frac{BE}{EC} [18:29] - Ex 6.2 Q5: In Fig. 6.20, DE \parallel OQ and DF \parallel OR. Show that EF \parallel QR [20:44] - Ex 6.2 Q6: In Fig. 6.21, A, B and C are points on OP, OQ and OR. Prove that BC \parallel QR [23:32] - Ex 6.2 Q7: Prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side (Theorem 6.1) [26:34] - Ex 6.2 Q8: Prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side (Theorem 6.2) [28:37] - Ex 6.2 Q9: ABCD is a trapezium in which AB \parallel DC and its diagonals intersect at O. Show that \frac{AO}{BO} = \frac{CO}{DO} [34:23] - Ex 6.2 Q10: Diagonals of a quadrilateral ABCD intersect at O such that \frac{AO}{BO} = \frac{CO}{DO}. Show that ABCD is a trapezium [38:22] - Ex 6.3 Q1: State which pairs of triangles in Fig. 6.34 are similar & write the similarity criterion [45:56] - Ex 6.3 Q2: In Fig. 6.35, \Delta ODC \sim \Delta OBA, \angle BOC = 125^\circ, \angle CDO = 70^\circ. Find \angle DOC, \angle DCO and \angle OAB [49:06] - Ex 6.3 Q3: Diagonals AC and BD of a trapezium ABCD with AB \parallel DC intersect at O. Using similarity, show that \frac{OA}{OC} = \frac{OB}{OD} [52:39] - Ex 6.3 Q4: In Fig. 6.36, \frac{QR}{QS} = \frac{QT}{PR} and \angle 1 = \angle 2. Show that \Delta PQS \sim \Delta TQR [55:46] - Ex 6.3 Q5: S and T are points on sides PR and QR of \Delta PQR such that \angle P = \angle RTS. Show that \Delta RPQ \sim \Delta RTS [59:15] - Ex 6.3 Q6: In Fig. 6.37, if \Delta ABE \cong \Delta ACD, show that \Delta ADE \sim \Delta ABC [01:04:07] - Ex 6.3 Q7: In Fig. 6.38, altitudes AD and CE intersect at P. Show similarity for all 4 parts [01:13:09] - Ex 6.3 Q8: E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that \Delta ABE \sim \Delta CFB [01:17:34] - Ex 6.3 Q9: In Fig. 6.39, \Delta ABC and \Delta AMP are two right triangles. Prove similarity & ratio \frac{CA}{PA} = \frac{BC}{MP} [01:19:52] - Ex 6.3 Q10: CD and GH are bisectors of \angle ACB and \angle EGF. If \Delta ABC \sim \Delta FEG, prove the 3 similarity relations [01:27:22] - Ex 6.3 Q11: In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC. If AD \perp BC and EF \perp AC, prove that \Delta ABD \sim \Delta ECF [01:29:03] - Ex 6.3 Q12: Sides AB, BC and median AD of \Delta ABC are proportional to sides PQ, QR and median PM of \Delta PQR. Show that \Delta ABC \sim \Delta PQR [01:34:35] - Ex 6.3 Q13: D is a point on side BC of \Delta ABC such that \angle ADC = \angle BAC. Prove that CA^2 = CB \times CD [01:37:05] - Ex 6.3 Q14: Sides AB, AC and median AD of \Delta ABC are proportional to sides PQ, PR and median PM of \Delta PQR. Prove that \Delta ABC \sim \Delta PQR [01:46:53] - Ex 6.3 Q15: A vertical pole of length 6 m casts a shadow 4 m long, while a tower casts a shadow 28 m long. Find the height of the tower [01:50:02] - Ex 6.3 Q16: If AD and PM are medians of \Delta ABC and \Delta PQR where \Delta ABC \sim \Delta PQR, prove that \frac{AB}{PQ} = \frac{AD}{PM} 📌 Key Highlights of This Lecture: Detailed proof and concept of Basic Proportionality Theorem (BPT / Thales Theorem). Step-by-step solutions to every question of NCERT Exercise 6.2 and Exercise 6.3. Easy tricks to identify similarity criteria (AA, SAS, SSS) and writing the correct corresponding vertices. Important board exam questions marked with step-by-step presentation guidelines. 🚀 Viral & Trending Hashtags: #Class10Maths #TrianglesClass10 #Class10Chapter6 #NCERTSolutions #CBSEBoard2027 #BoardExamPreparation #Exercise6_2 #Exercise6_3 #BPTTheorem #MathsClass10 #Dhanab #ViralMaths #OneShotMaths