Question

ABCD is a rectangle in which diagonal AC bisect angle a and angle c show that abcd is a square​

Answer 1

• in in rectangle ABCD where
• AC bisect angle a that angle 1 = 2 angle 2
• and ac bisect angle c that angle 3 = 2 angle 4
• to prove: ABCD is a square
• proof a square is a rectangle when all sides are equal
• Now,

AD||BC (opposite sides of parallelogram are parallel)

and AC as transversal

angle 1=angle 4(alternate angles)

• Now,

angle 1 = 2 angle and angle1 = angle 4

• Hence,

angle 2 = angle 4

• in triangle abc angle, 2 = angle 4

so,BC=AB(sides opposite to equal angles are equal).........(1)

but BC = AD and AB = DC(opposite sides of rectangle are equal)......(2)

from 1 and 2

• AB=BC=CD=DA

So, ABCD is a rectangle with all sides equal.

Hence, ABCD is a square .