Question

Show that the bisector of angles of a parallelogram form a rectangle.

Answer 1

Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC
To prove: LKJI is a rectangle
∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary
 
 
[Since sum of adjacent angles of a parallelogram are supplementary]
 
ΔABJ is a right triangle since its acute interior angles are complementary
Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90°
Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles
Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle.
Thus LKJI is a rectangle.

Answer 2

Answer:

refer the attachment .. hope it helps ..