Geometry: Angles & Shapes
Measuring & Types of Angles
Angles are measured in degrees (°) with a protractor. An acute angle is less than 90°, a right angle is 90°, and an obtuse angle is between 90° and 180°.
A straight angle is exactly 180°, a reflex angle is between 180° and 360°, and a complete angle is 360°.
- Acute < 90°, right = 90°, obtuse 90°–180°.
- Straight = 180°, reflex 180°–360°, complete = 360°.
Triangles & Quadrilaterals
Triangles are named by their sides: an equilateral triangle has 3 equal sides, an isosceles triangle has 2 equal sides, and a scalene triangle has no equal sides.
Quadrilaterals have 4 sides: a square (4 equal sides, 4 right angles), a rectangle, a rhombus (4 equal sides) and a parallelogram (opposite sides equal and parallel).
- Equilateral: 3 equal sides; isosceles: 2 equal; scalene: none equal.
- Square, rectangle, rhombus and parallelogram are quadrilaterals.
Circles & 3D Shapes (Euler's Formula)
For a circle, the distance around it is the circumference, a part of the curve is an arc, and a slice (like a pizza piece) is a sector.
For solid shapes, Euler's formula says Faces + Vertices − Edges = 2. A cube has 6 faces, 8 vertices and 12 edges: 6 + 8 − 12 = 2.
- Circle: circumference (around), arc (part of curve), sector (slice).
- Euler's formula: F + V − E = 2.