MathematicsThe bisector of interior angles of a parallelogram forms a rectangle.

The bisector of interior angles of a parallelogram forms a rectangle.

  1. A
    PQRS have a measure of  therefore, not  PQRS is a rectangle
  2. B
    PQRS have a measure of  therefore, PQRS is a rectangle
  3. C
    PQRS have a measure of  therefore, PQRS is a angle
  4. D
    PQRS have a measure of  therefore, PQRS is a rectangle 

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    Solution:

    Let us observe the triangle APB. We know that the opposite sides of a parallelogram are parallel.
    Therefore, AC ll BD and AB is the transversal.
    Now, angle A + angle (co – interior angles)
      Now, in a similar way, AC ll BD and CD is the transversal.
    So, by following the same method as shown above, we get the measure of angle R.
    R=Now, as we know that AB ll CD, therefore, the transversal is BD.
    angle B + angle  (co – interior angles)
    Now, in a similar way, AB ll CD and AC is the transversal.
    So, by following the same method as shown above, we get the measure of angle S.
    Angle S = So,
    Angle P = angle R = angle Q = angle S = We have  all the angles of PQRS have a measure of  Therefore, PQRS is a rectangle.
    So, option 4 is correct.
     
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