Question

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

Answer 1

PQRS is a rectangle
`angleP=angleQ=angleR=angleS=90^0`
`angleADC=theta`
`anglePDC=1/2angleADC=1/2theta`
`angleBCD=theta_1`
`anglePCD=1/2angleBCD=1/2theta_1`
`anglePCD+angleBCD=1/2theta+1/2theta_1=90^0`
`:.anglePCD+anglePDC+angleDPC=180^2`
`angleDPC=90^0`