Basic Geometry Guide for Students

This Basic Geometry Guide for Students is a simple and clear resource that covers essential concepts like angles, shapes, and key terms. Whether you’re preparing for a test or just starting out, this Basic Geometry Guide for Students offers an easy way to understand and review core geometry topics.

Types of Angles

• Acute Angle – Measures less than 90°
• Right Angle – Measures exactly 90°
• Obtuse Angle – Measures more than 90° but less than 180°
• Straight Angle – Measures exactly 180°
• Reflex Angle – Measures more than 180° but less than 360°
• Complete Angle – Measures exactly 360°
• Zero Angle – Measures 0°, both arms lie on the same line

Types of Triangles

Classified by Sides:

• Equilateral Triangle – All sides and angles are equal (each angle = 60°)
• Isosceles Triangle – Two equal sides and two equal angles
• Scalene Triangle – All sides and angles are different

Classified by Angles:

• Acute Triangle – All angles are less than 90°
• Right Triangle – Has one 90° angle
• Obtuse Triangle – Has one angle greater than 90°

Types of Quadrilaterals

• Square – 4 equal sides, 4 right angles
• Rectangle – Opposite sides equal, all angles are 90°
• Rhombus – All sides equal, opposite angles equal (no right angle unless a square)
• Parallelogram – Opposite sides equal and parallel, opposite angles equal
• Trapezium (US: Trapezoid) – One pair of opposite sides parallel
• Isosceles Trapezium – Non-parallel sides are equal, base angles are equal
• Kite – Two pairs of adjacent equal sides, one pair of opposite angles equal

Key Circle Geometry Terms

• Center – The fixed middle point of a circle
• Radius – Distance from the center to any point on the circle
• Diameter – Longest straight line through the center (2 × radius)
• Chord – A line segment joining two points on the circle
• Arc – A curved part of the circle’s boundary
• Sector – A “slice” formed by two radii and an arc
• Segment – The region between a chord and the arc above it
• Circumference – Total perimeter or boundary length of the circle
• Pi (π) – The constant ratio of a circle’s circumference to its diameter (≈ 3.14159)
• Tangent – A line that touches the circle at exactly one point

Common 3D Geometric Shapes

• Cube – 6 equal square faces, 12 edges, 8 vertices
• Cuboid (Rectangular Prism) – 6 rectangular faces
• Sphere – Perfectly round shape (like a ball), no edges or corners
• Cylinder – 2 circular faces and 1 curved side
• Cone – 1 circular base tapering to a point (vertex)
• Triangular Prism – 2 triangular and 3 rectangular faces
• Pyramid – Polygon base with triangular faces meeting at a single point (apex)

Fundamental Geometry Terms

• Point – An exact position in space, has no size
• Line – A straight path that extends infinitely in both directions
• Line Segment – A part of a line with two fixed endpoints
• Ray – A line that starts at one point and extends infinitely in one direction
• Parallel Lines – Lines that never meet, always the same distance apart
• Perpendicular Lines – Lines that intersect at right angles (90°)
• Angle Bisector – A line dividing an angle into two equal parts
• Altitude of Triangle – Perpendicular from a vertex to the opposite side
• Median of Triangle – Connects a vertex to the midpoint of the opposite side
• Centroid – Point where the medians of a triangle intersect
• Orthocenter – Point where all altitudes of a triangle meet
• Incenter – Point where all angle bisectors of a triangle intersect (center of inscribed circle)
• Circumcenter – Point equidistant from all triangle vertices (center of circumscribed circle)
• Polygon – A closed 2D figure with straight sides (e.g., triangle, hexagon)
• Regular Polygon – A polygon with all sides and angles equal