Imagine that the rectangle is rotated counterclockwise. make a conjecture as to which properties of a figure stay the same after the rotation.

The rotation described in the problem is known as a rigid transformation, which refers to all transformation that doesn't change the shape or size of the object, like this case.

Basically, the rectangle after the counterclockwise rotation maintains its side lengths, its angle, but changes its vertices, that is, its coordinates without altering its dimension. This conjecture englobes all important qualities of the rectangle.

Therefore, the properties that remain the same after rotation are angles, sides and shape.

the answer is simply just 6n add the two together as they have an n

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.