Question

Using ruler and compasses only, construct a rectangle each of whose diagonals measures 6 cm and the diagonals intersect at an angle of 45°.​

Answer 1

In a rectangle ,

diagonals bisect each other.

so first draw a line , say AC = 6 cm.

now find its midpoint, say O.

either by drawing a perpendicular bisector of it , which will intersect it at O.

or just by taking a point at 3 cm distance from A or C.

now from O.

construct an angle of angle AOB =  45 degree with the help of compass.

you can draw this by making 90 degree angle then bisecting it.

cut AO = 3 cm, now produce AO to D , where OD = 3 cm.

now you have all four vertices, A, B, C and D, now

join

AB, BC, CD and AD,

ABCD is your required ABCD . where diagonal of each 6 cm length. and intersecting at 45 degree angle.

if needed i can show on video

Step-by-step explanation: