Lines and Angles – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 6 in Mathematics.
This one-pager compiles key formulas and equations from the Lines and Angles chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Line Segment: AB = |A - B|
AB represents the distance between point A and point B. This formula provides the length of the line segment formed by two endpoints, A and B.
Angle Sum Property: Sum of Angles in a Triangle = 180°
This property states that the sum of the interior angles of a triangle is always 180 degrees. It helps in determining unknown angles when given two angles.
Complementary Angles: ∠A + ∠B = 90°
If two angles, A and B, are complementary, their sum equals 90 degrees. This is useful for solving problems involving right angles.
Supplementary Angles: ∠A + ∠B = 180°
When two angles A and B add up to 180 degrees, they are supplementary. This concept is key in understanding linear pairs.
Vertical Angles: ∠A = ∠C and ∠B = ∠D
Vertical angles are opposite angles formed by intersecting lines and are always equal. This property is instrumental in proofs.
Sum of Angles on a Straight Line: ∠A + ∠B = 180°
Angles A and B on a straight line add up to 180 degrees. This helps in determining angles in linear configurations.
Angle in Right Triangle: ∠A + ∠B + ∠C = 180°
In any right triangle, the sum of the three angles is always 180 degrees. This helps ascertain unknown angle measures.
Measurement of an Angle: Degree (°)
Angles are measured in degrees. This unit is fundamental for angle calculations in various geometric problems.
Equation of a Line: y = mx + c
In this linear equation, m is the slope and c is the y-intercept. It describes the relationship between x and y coordinates.
Identifying Angles: ∠DBE, ∠EBD
Angles can be named using the vertex and points on the rays. This nomenclature is crucial for clarity in geometric discussions.
Equations
Angle Measure: m∠A = ∠B
This equation indicates that angle A is measured equal to angle B. Useful in solving angle-related problems.
Number of Lines through a Point: Infinite
Through any given point, an infinite number of lines can be drawn. This concept is foundational in understanding points and lines.
Parallel Lines: l || m
Lines l and m are parallel if they never intersect. Understanding this property aids in many geometric proofs.
Angle Relationships: ∠A + ∠B = 180° (Linear Pair)
In a linear pair of angles, the sum equals 180 degrees. This is key in identifying angle relationships.
Sum of Angles in a Polygon: (n - 2) × 180°
The sum of all interior angles in a polygon with n sides can be computed using this formula, aiding in polygonal geometry.
Equilateral Triangle Angles: ∠A = ∠B = ∠C = 60°
In an equilateral triangle, each angle measures 60 degrees. This helps in understanding properties of triangles.
Scalene Triangle: All sides and angles unequal
A scalene triangle has no equal sides or angles. Identifying this helps in classifying triangles.
Obtuse Angle: 90° < ∠A < 180°
An angle A is obtuse if it is greater than 90 degrees but less than 180 degrees. This classification is essential in angle studies.
Acute Angle: 0° < ∠A < 90°
An angle A is acute if it is less than 90 degrees. Recognizing this type is vital for angle categorization.
Reflex Angle: 180° < ∠A < 360°
A reflex angle A is greater than 180 degrees but less than 360 degrees. This understanding assists in advanced angle geometry.
