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Topic Content:

  • Parallelograms
  • Rhombus
  • Rectangle
  • Kite
  • Square

1. Parallelogram:

This is a quadrilateral which has both pairs of opposite sides parallel.

Screenshot 2022 05 17 at 11.27.21

Properties of Parallelogram:

  • The opposite sides are parallel
  • The opposite sides are equal |AD| = |BC|, |AB| = |DC|
  • The opposite angles are equal Y2 = Y1, X2 = X1
  • The diagonals bisect one another

2. Rhombus:

Screenshot 2022 05 17 at 11.50.35

Properties of Rhombus:

  • All four sides are equal
  • The opposite sides are parallel
  • The opposite angles are equal (∠S = ∠Q, ∠P = ∠R)
  • The diagonals bisect the angles
  • Adjacent angles are supplementary (e.g., ∠S + ∠R = 180°).

3. Rectangle:

rectangle

Properties of Rectangle:

  • All of the properties of a parallelogram are found
  • All four angles are right angles
  • The diagonals are equal

Kite:

KITE quad

Properties of a Kite:

  • Diagonals bisect at right angles
  • Only one pair of opposite angles is equal
  • Each pair of adjacent sides is equal

Square :

Screenshot 2022 05 17 at 12.17.23

Properties of a Square:

  • All of the properties of a rhombus are found
  • All four angles are right angles
  • The diagonals are equal

Example 3.1.1:

RSTUV is a regular pentagon. Find the angle of RUV.

regular pentagon

Solution:

Join R to U

Screenshot 2022 05 17 at 12.33.31

 

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