Geometry Basics

Geometry

Points, Lines, and Planes

• A point is a location in space, represented by a set of coordinates (x, y, z)
• A line is a set of points extending infinitely in two directions
• A plane is a flat surface that extends infinitely in all directions

Angles and Measurements

• An angle is formed by two rays sharing a common endpoint (vertex)
• Types of angles:
  • Acute angle: less than 90°
  • Right angle: exactly 90°
  • Obtuse angle: greater than 90° but less than 180°
  • Straight angle: exactly 180°
• Measurements:
  • Degree: a unit of angle measurement (1° = 1/360 of a circle)
  • Radians: a unit of angle measurement (1 radian = 180° / π)

Properties of 2D Shapes

• Properties of triangles:
  • Angles: sum of interior angles = 180°
  • Sides: sum of any two sides > third side
• Properties of quadrilaterals:
  • Rectangles: all angles are right angles
  • Squares: all sides are equal, all angles are right angles
• Properties of circles:
  • Center: fixed point equidistant from all points on the circle
  • Radius: distance from center to any point on the circle
  • Circumference: distance around the circle (2πr)

3D Shapes

• Types of 3D shapes:
  • Pyramids: triangular base, triangular sides
  • Prisms: rectangular base, rectangular sides
  • Spheres: set of points equidistant from a central point
• Properties of 3D shapes:
  • Surface area: sum of areas of all faces
  • Volume: amount of space inside the shape

Geometry

Fundamentals

• A point is a location in space, represented by a set of coordinates (x, y, z)
• A line is a set of points extending infinitely in two directions
• A plane is a flat surface that extends infinitely in all directions

Angles

• An angle is formed by two rays sharing a common endpoint (vertex)
• Angles can be classified into:
  • Acute angles (less than 90°)
  • Right angles (exactly 90°)
  • Obtuse angles (greater than 90° but less than 180°)
  • Straight angles (exactly 180°)

Measurements

• A degree is a unit of angle measurement (1° = 1/360 of a circle)
• A radian is a unit of angle measurement (1 radian = 180° / π)

Properties of 2D Shapes

• Triangles:
  • The sum of interior angles is 180°
  • The sum of any two sides is greater than the third side
• Quadrilaterals:
  • Rectangles have all angles as right angles
  • Squares have all sides equal and all angles as right angles
• Circles:
  • The center is a fixed point equidistant from all points on the circle
  • The radius is the distance from the center to any point on the circle
  • The circumference is the distance around the circle (2πr)

3D Shapes

• Types of 3D shapes include:
  • Pyramids (triangular base, triangular sides)
  • Prisms (rectangular base, rectangular sides)
  • Spheres (set of points equidistant from a central point)
• Properties of 3D shapes include:
  • Surface area is the sum of areas of all faces
  • Volume is the amount of space inside the shape

Hindi Grammar

Script and Orthography

• Hindi uses the Devanagari script, written from left to right.
• The script consists of 47 characters: 14 vowels, 32 consonants, and 1 special character (avagraha).

Nouns

• Hindi nouns are classified into three categories: masculine, feminine, and neuter.
• Nouns have two numbers: singular and plural.
• Case endings are used to indicate grammatical function, including:
  • Nominative (subject)
  • Accusative (direct object)
  • Genitive (possessor or attribute)
  • Dative (indirect object)
  • Ablative (means or instrument)
  • Locative (location)

Verbs

• Hindi verbs are inflected for:
  • Tense: present, past, and future
  • Aspect: simple, progressive, and perfect
  • Mood: indicative, imperative, and subjunctive
  • Voice: active and passive

Sentence Structure

• Hindi sentence structure is typically Subject-Object-Verb (SOV).
• Word order can change depending on context and emphasis.
• Participles and conjunctive participles are used to connect clauses.

Postpositions

• Hindi postpositions are used to indicate grammatical relationships between nouns and other words.
• Common postpositions include:
  • के (ke)
  • से (se)
  • में (meṁ)
  • पर (par)

Honorifics

• Hindi has a system of honorifics to show respect or politeness.
• Honorifics are used with verbs, nouns, and pronouns to indicate respect or deference.
• The use of honorifics depends on the speaker's relationship with the listener or subject.