Exercise 8.2 Class 10 Math Solutions – Arc, Chord & Central Angle Theorems, Punjab Board
Solved Exercise 8.2 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering Theorems 6 to 9 on congruent arcs, equal chords, and central angles in single and congruent circles with complete geometric proofs.
Exercise Overview
Exercise 8.2 in Unit 8: Chords and Arcs of a Circle of Class 10 Punjab Board Mathematics focuses on the direct and converse relationships linking circular arcs, chords, and central angles. This exercise delivers rigorous mathematical proofs establishing how arc congruence dictates linear chord equality and angular central symmetry.
The exercise systematically covers four major Euclidean theorems: Theorem 6 (congruent arcs yield equal chords), Theorem 7 (equal chords subtend congruent arcs), Theorem 8 (equal chords subtend equal central angles), and Theorem 9 (equal central angles are subtended by equal chords). By constructing triangles with radii and applying SAS and SSS triangle congruence postulates, students develop a logical framework for deductive geometric reasoning across both single circles and pairs of congruent circles.
In Punjab Board examinations across Lahore, Faisalabad, Rawalpindi, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan, Theorems 6 through 9 and their rider problems are prominent questions in the compulsory geometry theorem portion of Section C. Mastering these step-by-step proofs equipped with exact diagrams and valid axiomatic justifications guarantees full marks in board exams.