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Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles

definition

Quadrilaterals: A four-sided polygon is a quadrilateral. Any four points in a plane, out of which three are non-collinear are joined in order to formed a four-sided closed figure called ‘quadrilateral’.

notes

Quadrilaterals:

  • Any four points in a plane, out of which three are non-collinear are joined in order to formed a four-sided closed figure called ‘quadrilateral’.
  • A quadrilateral has four sides, four angles and four vertices. Quadrilateral could be regular or irregular.
  • A four-sided polygon is a quadrilateral.

  • Quadrilateral ABCD has four sides `bar"AB", bar"BC", bar"CD", and bar"DA"`.
  • It has four angles ∠A, ∠B, ∠C, and ∠D.
  • A, B, C and D are the four vertices and
  • BD and AC are the two diagonals of the quadrilateral ABCD.

Reading and Writing of a Quadrilateral:

  • A quadrilateral can be named by starting at any vertex and going serially either clockwise or anti-clockwise around the figure.

  • When writing the name of a quadrilateral a sign like this ‘□’ is put in place of the word ‘quadrilateral’.

Clockwise Anti-clockwise
Reading Writing Reading Writing
Quadrilateral MNOP □ MNOP Quadrilateral PONM □ PONM
Quadrilateral NOPM □ NOPM Quadrilateral ONMP □ ONMP
Quadrilateral OPMN □ OPMN Quadrilateral NMPO □ NMPO
Quadrilateral PMNO □ PMNO Quadrilateral MPON □ MPON

1. Adjacent Sides of a Quadrilateral:

  • Adjacent sides of the quadrilateral have a common vertex.
  • The sides MN and MP of □ MNOP have a common vertex M. Sides MN and MP are adjacent sides.
  • Every quadrilateral has four pairs of adjacent sides.

Pairs of adjacent sides:

  1. Side MN and Side MP

  2. Side MN and Side NO

  3. Side NO and Side OP

  4. Side OP and Side MP.

2. Opposite Sides of a Quadrilateral:

  • Opposite sides of the quadrilateral do not have a common vertex.
  • In □  MNOP the sides MP and NO have no common vertex.
  • Side MP and side NO are opposite sides of the quadrilateral.

Pairs of opposite sides:

  1. sides MP and NO

  2. sides MN and PO

3. Adjacent Angles of a Quadrilateral:

  • The angles of a quadrilateral which have one common arm are called adjacent angles of the quadrilateral.
  • These angles are neighbouring or adjacent angles.

Name the adjacent angles of the quadrilateral MNOP.

  1. ∠MNO and ∠PMN

  2. ∠MPO and ∠NOP

  3. ∠PON and ∠MNO

  4. ∠ONM and ∠PMN

4. Opposite Angles of a Quadrilateral:

  • The angles of a quadrilateral which do not have a common arm are called opposite angles of a quadrilateral.
  • They lie opposite to each other.

Pair of Opposite angle:

  1. Angle opposite to ∠PMN is ∠NOP.
  2. Angle opposite to ∠MNO is ∠OPM.

5. Diagonals of a Quadrilateral:

  • The line segments which join the vertices of the opposite angles of a quadrilateral are the diagonals of the quadrilateral.
  • The segments MO and NP are the diagonals of the quadrilateral ABCD.

6. Interior & Exterior of A Quadrilateral:

                   

  • Being a polygon, a quadrilateral has an exterior and an interior.
  • P, Q, and R are in the interior of the quadrilateral, M and L are in the exterior, and A, B, C, D, and E on the quadrilateral.
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