Geometry | Professor Porua https://www.professorporua.squaryum.com Squaryum's Educational Guide Wed, 15 Oct 2025 07:03:43 +0000 en-US hourly 1 https://wordpress.org/?v=6.9.1 https://www.professorporua.squaryum.com/wp-content/uploads/2024/01/cropped-Logo-500-32x32.png Geometry | Professor Porua https://www.professorporua.squaryum.com 32 32 Pythagoras’ Theorem https://www.professorporua.squaryum.com/geometry/pythagoras-theorem/ Thu, 25 Jan 2024 11:15:37 +0000 https://www.professorporua.squaryum.com/?p=394

Pythagoras’ Theorem or Pythagorean Theorem is named after a Greek philosopher, Pythagoras, who was born around 507 BC in Samos island of old Greece.

According to the diagram:
∠ABC = 90° (AB is perpendicular to BC) & AC is Hypotenuse then:

(AC)² = (AB)² + (BC)²

OR

c² = a² + b²

OR

(Hypotenuse)² = (Perpendicular)² + (Base)²

]]> Area Perimeter https://www.professorporua.squaryum.com/geometry/area-perimeter/ Wed, 24 Jan 2024 07:46:32 +0000 https://www.professorporua.squaryum.com/?p=368

Area:

Space occupied by a shape inside it’s boundary.

Perimeter:

Walking distance along the boundary of the  shape.
π [Pi] (Mathematical Constant) = 3.14 or ⁠22/7
Shapes can be square, rectangle, triangle, circle & others.
There are many other shapes, which you will know in another chapter.
]]> Types of Triangle https://www.professorporua.squaryum.com/geometry/types-of-triangle/ Mon, 22 Jan 2024 14:46:47 +0000 https://www.professorporua.squaryum.com/?p=333

Equilateral Triangle:

AB=BC=AC
(all 3 sides of a triangle are equal)

Isosceles Triangle:

AB=AC or AB=BC or BC=AC
(any 2 sides of a triangle are equal)

Scalene Triangle:

None of the sides of a triangle are equal

Acute-Angled Triangle:

a<90°, b<90°, c<90°
(all 3 angles of a triangle are between 0° & 90°)

Right-Angled Triangle:

a=90° or b=90° or c=90°
(any 1 angle of a triangle is 90°)

Obtuse-Angled Triangle:

a>90° or b>90° or c>90°
(any 1 angle of a triangle is between 90° & 180°)
]]> Lines & Angles https://www.professorporua.squaryum.com/geometry/linesangles/ Mon, 22 Jan 2024 12:09:00 +0000 https://www.professorporua.squaryum.com/?p=319

Parallel Lines:

Lines which never meet at any point and maintain same distance between them.

Transversal Line:

A line which intersects 2 or more lines at distinct points. Different angles are formed at those points.

Types of Angles:

  • Acute Angle (angle value between 0° & 90°)
  • Right Angle (angle is exactly 90°)
  • Obtuse Angle (angle value between 90° & 180°)
  • Reflex Angle (angle value between 180° & 360°)
Other such angles are
  • Straight Angle (angle is exactly 180°, which is a straight line)
  • Complete Angle (angle is exactly 360°, which is a straight line)

Types of Related Angles:

  • Complementary Angles (sum of 2 angles = 90°)
  • Supplementary Angles (sum of 2 angles = 180°)
    m + n = 180° | n + o = 180° | o + p = 180° | p + m = 180°
    q + r = 180° | r + s = 180° | s + t = 180° | t + q = 180°
  • Alternate Interior Angles (2 angles, on opposite sides of a transversal line inside 2 parallel lines, are equal)
    r = p | q = o
  • Alternate Exterior Angles (2 angles, on opposite sides of a transversal line outside 2 parallel lines, are equal)
    t = n | s = m
  • Corresponding Angles (2 angles, on the same relative position of 2 parallel lines along a transversal line at each intersection points, are equal)
    m = q | n = r | o = s | p = t
  • Vertically Opposite Angles (2 angles, which are on vertically opposite sides at the same intersection point, are equal)
    m = o | n = p | q = s | r = t
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