Question

if two parallel lines are intersected by a transversal then prove that the bisector of interior angles form a rectangle.​

Answer 1

here LSllMT and p is a transversal

R. T. P. DBCD is a Rectangle .

Proof'' angleLAC = angleACT (A.I.A.)

diveded by 2 both side

so angleBAC = angleACD

similarly angleACB = angle ACD

since A.I.A. on the same side of the transversal are equal .

so BCllAD

and BAllCD

hence it is a llgm

Now,

angle LAC + angleACS =180 (By linear pair )

divided by 2 both side so

angleBAC + angleCAD =90

so angleBAD =90degree

hence,

ABCD is a rectangle. (H.P.)

Answer 2

Answer:

ere LSllMT and p is a transversal

R. T. P. DBCD is a Rectangle .

Proof'' angleLAC = angleACT (A.I.A.)

diveded by 2 both side

so angleBAC = angleACD

similarly angleACB = angle ACD

since A.I.A. on the same side of the transversal are equal .

so BCllAD

and BAllCD

hence it is a llgm

Now,

angle LAC + angleACS =180 (By linear pair )

divided by 2 both side so

angleBAC + angleCAD =90

so angleBAD =90degree

hence,

ABCD is a rectangle. (H.P.)

Step-by-step explanation: