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The angle bisectors of a parallelogram f...

The angle bisectors of a parallelogram form a rectangle.

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AD||BC and AB is traversal
`/_A+/_B=180^@`
`1/2/_A+1/2/_B=90^@`
`/_BAS+/_ABS=90^@`
`In/_ABS`
`/_BAS+/_ABS+/_ASB=180^@`
`90^@+/_ASB=180^@`
`/_ASB=90^@`
...
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Knowledge Check

  • Three statements are given below: I. In a ||gm, the angle bisectors of two adjacent angles enclose a right angle. I. The angle bisectors of a ||gm form a rectangle. III. The triangle formed by joining the midpoints of the sides of an isosceles triangle is not necessarily an isosceles triangle. Which is true?

    A
    I only
    B
    II only
    C
    I and II
    D
    II and III

  • Consider the following statements 1. The bisectors of all the four angles of a parallelogram enclose a rectangle. 2. The figure formed by joining the midpoints of the adjacent sides of a rectangle is a rhombus. 3. The figure formed by joining the midpoints of the adjacent sides of a rhombus is a square. Which of these statements are correct ?

    A
    1 and 2
    B
    2 and 3
    C
    3 and 1
    D
    1, 2 and 3

  • The bisector of the angles of a parallelogram enclose a

    A
    rectangle
    B
    rhombus
    C
    square
    D
    trapezium

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    The figure formed by joining the mid-point of the adjacent sides of a parallelogram is a rectangle (b) parallelogram (c) rhombus (d) square

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    Complete each of the following statements by means of one of those given in brackets again each: If one pair of opposite sides are equal and parallel, then the figure is ............... (parallelogram, rectangle, trapezium) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is .............. (square, rectangle, trapezium) A line drawn from the mid-point of one side of a triangle .................. another side intersects the third side at its mid-point. (perpendicular to, parallel to, to meet) If one angle of a parallelogram is a right angle, then it is necessarily a .................... (rectangle, square, rhombus) Consecutive angles of parallelogram are ...................... (supplementary, complementary) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily (rectangle, parallelogram, rhombus) if opposite angles of a quadrilateral are equal, then it is necessarily a ................... (parallelogram, rhombus, rectangle) If consecutive sides of a parallelogram are equal, then it is necessarily a ............. (kite, rhombus, square)

    The bisector of the angles of a parallelogram enclose a ..................

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