Review: properties of quadrilaterals

key notes :

🔹 Quadrilaterals – Overview

  • A quadrilateral is a polygon with 4 sides and 4 angles. 🟦
  • Sum of interior angles: 360° ➕
  • Can be convex (all angles < 180°) or concave (one angle > 180°). 🔺

🔹 Types of Quadrilaterals & Properties

1️⃣ Square ⬜

  • All sides equal ➖
  • All angles 90° ➕
  • Opposite sides are parallel ↔️
  • Diagonals are equal & bisect at 90° ✖️

2️⃣ Rectangle ▭

  • Opposite sides equal & parallel ↔️
  • All angles 90° ➕
  • Diagonals are equal but do not bisect at 90° ✖️

3️⃣ Rhombus ♦️

  • All sides equal ➖
  • Opposite angles are equal ↔️
  • Diagonals bisect each other at 90° ✖️
  • Diagonals not equal ❌

4️⃣ Parallelogram ▱

  • Opposite sides equal & parallel ↔️
  • Opposite angles are equal ↔️
  • Diagonals bisect each other but not necessarily equal ✖️

5️⃣ Trapezium / Trapezoid 🔺

  • Only one pair of opposite sides parallel ↔️
  • Non-parallel sides are called legs
  • Angles adjacent to the same leg are supplementary ➕

6️⃣ Kite 🪁

  • Two pairs of adjacent sides equal ➖
  • One pair of opposite angles equal ↔️
  • Diagonals perpendicular ✖️
  • One diagonal bisects the other

🔹 Quick Tips 💡

  • Diagonals: Check if they are equal or perpendicular. ✖️
  • Angles: Check if all 90° or opposite angles equal. 🔄
  • Sides: Look for equal sides or parallel sides ↔️

Learn with an example

Is parallelogram GHIJ a rhombus?

  • yes
  • no

Since ∠GHJ ≅ ∠GJH ≅ ∠HJI ≅ ∠IHJ, HJ bisects ∠GHI and ∠GJI.

So, GHIJ is a rhombus.

Is parallelogram DEFG a rhombus?

  • yes
  • no

Since ∠EG F= ∠DEG = 46° and ∠DGE = ∠FEG = 48°, EG does not bisect ∠DGF and ∠DEF.

So, DEFG is not a rhombus.

Is parallelogram WXYZ a rhombus?

  • yes
  • no

Since ∠YVZ = 88°, WY and XZ are not perpendicular.

So, WXYZ is not a rhombus.

Let’s practice!