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<-- Basic Geometry | Polygons --> - Coggle Diagram
<-- Basic Geometry | Polygons -->
Types Of Angles
Obtuse Angle
Straight Angle
Right Angle
Acute Angle
Reflex Angle
Construction of Triangle
A triangle can be constructed given:
(a) 1 side and 2 angles
(b) 3 sides
(c) 2 sides and one angle
For (c), sometimes, it is possible to construct two different triangles
Complementary and Supplementary Angles
Complementary Angles
Two angles that add up to 90°
Supplementary Angles
Two angles that add up to 180°
Properties of Angles Formed by Intersecting Lines
The sum of angles at a point is 360° (∠s at a point)
Vertically opposite angles are equal (vert. opp. ∠s)
The sum of adjacent angles on a straight line is 180° (adj. ∠s on a str. line)
Properties of Angles Formed by Two Parallel Lines and A Transversal
If two parallel lines, PQ and RS, are cut by a transversal LM, then
Alternate angles are equal, e.g. ∠c = ∠d (alt. ∠s, PQ // RS)
Interior angles are supplementary, e.g. ∠b + ∠d = 180° (int. ∠s, PQ // RS
Corresponding angles are equal, e.g. ∠a = ∠b (corr. ∠s, PQ // RS)
Properties of Polygons
Sum of interior angles of an n-sided polygon = (n - 2) × 180°
Sum of exterior angles of an n-sided polygon = 360°
In a polygon, interior angle + exterior angle = 180°
Properties of Triangles
Angles sum of triangle: The sum of interior angles of a triangle is 180° (∠ sum of Δ)
Exterior angle of triangle: An exterior angle of a triangle is equal to the sum of its interior opposite angles (ext. ∠ of Δ)
Construction of Quadrilateral
We make use of the properties of special quadrilaterals (e.g. parallelogram and rectangle) to construct them
Properties of Quadrilaterals
Angle sum of quadrilateral: The sum of the interior angles of a quadrilateral is 360° (∠ sum of quad.)
Special Quadrilaterals
Order of Rotational Symmetry
Parallelogram: 2
Rectangle: 2
Rhombus: 2
Square: 4
Kite: 1 (no rotational symmetry)
Special Quadrilateral
Rectangle
Rhombus (special type of parallelogram and kite)
Parallelogram (special type of trapezium)
Square (special type of rectangle and rhombus)
Kite
:
Line(s) of Symmetry
Parallelogram: 0
Rectangle: 2
Rhombus: 2
Square: 4
Kite: 1
Diagonals
Rectangle: Bisect each other and are equal in length
Rhombus: Bisect each other at 90° and bisect the interior angles
Parallelogram: Bisect each other
Square: Bisect each other at 90°, are equal in length and bisect the interior angles
Kite: Cut each other at 90° and one of them bisects the interior angles
