Revision Notes: Triangles and Quadrilaterals | Mathematics Class 6 ICSE PDF Download

Triangles

Classification based on sides

Classification based on angles

Properties of Triangles

Quadrilaterals

A quadrilateral is a plane figure bounded by four straight lines. 

Properties of Quadrilaterals

• The sum of the four interior angles of a quadrilateral = 360 degrees 
• Its two diagonals intersect. 
• The line joining the midpoints of any two adjacent sides is parallel to the corresponding diagonal 
• Lines joining the midpoints of the sides of a quadrilateral in an order form a Parallelogram. 

Properties of a Parallelogram

• Opposite angles are equal. 
• Diagonals bisect each other. 
• The angles on the same side are supplementary 
• Each diagonal bisects the parallelogram into two congruent triangles 
• The angle bisectors of the opposite vertices are parallel 
• The angle between the  angular bisectors of the same side is a right angle 

Properties of a Trapezium

• Diagonals intersect each other 
• The line joining the midpoints of non-parallel sides is parallel to the parallel side, and its length is half of the sum of the parallel sides. 
• An isosceles trapezium has non-parallel sides equal, and it can be inscribed in a circle. 

Properties of a Rectangle 

Properties of a Kite 
A kite is a quadrilateral which has two pairs of adjacent sides equal. 

Properties of a Square
(i) Diagonals are equal and bisect at right angles. 
(ii) Diagonals bisect the opposite angles. 
(iii) Each diagonal divides the square into two congruent isosceles right-angled triangles. 
(iv) It can be inscribed in a circle 
(v) A circle can be inscribed in a square touching all its sides. 

Properties of a Rhombus 
​(i) All sides are equal 
(ii) Opposite angles are equal.
(iii) Diagonals bisect each other perpendicularly. 
(iv) Diagonals are bisectors of the angles at the corresponding vertices. 

• Theorem: If a pair of opposite sides of a quadrilateral are equal and parallel, it is a parallelogram 
• Theorem: In a parallelogram, opposite sides are equal, opposite angles are equal, and each diagonal bisects the parallelogram 
• Theorem: The diagonals of a parallelogram bisect each other.

Polygons

A polygon is a closed figure formed by line segments, such that: 

• Two line segments intersect only at their endpoints.