This mathematics formula guide for Class 10 focuses on triangles, which are three-sided closed figures. Triangles can be classified based on sides (scalene with no equal sides, isosceles with two equal sides, and equilateral with all sides equal) or angles (acute with all angles acute, right-angled with one right angle, and obtuse-angled with one obtuse angle). The concept of triangle similarity, where triangles have the same shape but not necessarily the same size, is introduced, with similarity based on equal corresponding angles and proportional corresponding sides. The Basic Proportionality Theorem (Thales Theorem) and its converse relate to lines intersecting or dividing the triangle’s sides. The AAA and SSS rules define the criteria for triangle similarity. Key triangle formulas include the area (A = 1/2 × base × height) and the perimeter (P = sum of the sides). Class 10 also covers triangle and circle theorems like Pythagoras’ Theorem, Midpoint Theorem, Angle Bisector Theorem, and others. The area of a triangle encompasses the entire region within its three sides. Congruency rules are also mentioned, including SSS, SAS, ASA, and AAS.