Important formulas for Geometry in Math Class 10
Properties of Points, Lines, and Planes
1. Distance Formula: The distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)^2 + (y2 - y1)^2)
2. Midpoint Formula: The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2)
Angles and Measurements
1. Sum of Interior Angles of a Triangle: 180°
2. Sum of Exterior Angles of a Triangle: 360°
3. Angle Sum Property of a Quadrilateral: 360°
Properties of Triangles
1. Pythagorean Theorem: a^2 + b^2 = c^2 (where a and b are the legs and c is the hypotenuse of a right triangle)
2. Area of a Triangle: (base × height) / 2
3. Perimeter of a Triangle: a + b + c (where a, b, and c are the sides of the triangle)
Properties of Quadrilaterals
1. Area of a Parallelogram: base × height
2. Area of a Rectangle: length × width
3. Area of a Rhombus: (diagonal1 × diagonal2) / 2
4. Perimeter of a Quadrilateral: a + b + c + d (where a, b, c, and d are the sides of the quadrilateral)
Properties of Circles
1. Circumference of a Circle: 2πr (where r is the radius of the circle)
2. Area of a Circle: πr^2 (where r is the radius of the circle)
3. Arc Length of a Circle: (θ/360) × 2πr (where θ is the central angle and r is the radius of the circle)
Coordinate Geometry
1. Distance Formula: √((x2 - x1)^2 + (y2 - y1)^2)
2. Section Formula: ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)) (where (x1, y1) and (x2, y2) are the coordinates of the points and m:n is the ratio of the division)
These formulas are essential for solving geometric problems in Class 10 Math. Practice using them to become proficient!
