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ICSE-VIII-Mathematics

17: Special Types of Quadrilaterals Class 8 Maths

with Solutions -
Qstn# A-11 Prvs-QstnNext-Qstn
  • #11
    ABCD is a parallelogram. What kind of quadrilateral is it if : (i) AC = BD and AC is perpendicular to BD? (ii) AC is perpendicular to BD but is not equal to it? (iii) AC = BD but AC is not perpendicular to BD?
    Ans : (i)
    AC = BD (Given)
    & AC ⊥ BD (Given)
    i.e., Diagonals of quadrilateral are equal and they are ⊥r to each other.
    ∴ ABCD is square. (ii)
    AC ⊥BD (Given)
    But AC & BD are not equal
    ∴ ABCD is a Rhombus. (iii)
    AC = BD but Ac & BD are not ⊥r to each other.
    ∴ ABCD is a rectangle.
  • #11-i
    AC = BD and AC is perpendicular to BD?
    Ans :
    AC = BD (Given)
    & AC ⊥ BD (Given)
    i.e., Diagonals of quadrilateral are equal and they are ⊥r to each other.
    ∴ ABCD is square.
  • #11-ii
    AC is perpendicular to BD but is not equal to it?
    Ans :
    AC ⊥BD (Given)
    But AC & BD are not equal
    ∴ ABCD is a Rhombus.
  • #11-iii
    AC = BD but AC is not perpendicular to BD?
    Ans :
    AC = BD but Ac & BD are not ⊥r to each other.
    ∴ ABCD is a rectangle.