Question

prove that the bisectors of interior angles of a parallelogram form a rectangle

Answer 1

∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary
 
∠BAJ = ∠BAD because AE bisects ∠BAD
       
∠ABJ = ∠ABC because DH bisects ∠ABC
 
∠BAJ + ∠ABJ = 90° halves of supplemetary angles are complementary
 
ᐃABJ is a right triangle because its acute interior angles are complementary
 
In a same way in ᐃCDL, ∠DLC = 90° and in ᐃADI,  ∠AID = 90°
Then ∠JIL = 90°
as, 
∠AID and ∠JIL are vertical angles
Three angles are right angles in quadrilaterals as well as the fourth one. so LKJI is a rectangle.  

Answer 2

Answer:

To prove: MNOP is a rectangle.

In parallelogram ABCD

∠A=∠D=90°

[they form a straight line]

∴IN△AMD,∠M=90°

∠M=∠N=90°

[they form a straight line]

Similarly,

∠M=∠P=90°

And

∠P=∠O=90°

∴∠MPO=∠PON∠ONM=∠NMO=90°

∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90°]

Step-by-step explanation:

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