\(ABCD\) is a rectangle with \(AB = 12\) cm and \(BC = 9\) cm. (a) Write down the mathematical name of angle \(ABC\). [1] (b) Work out the perimeter of \(AB...

(a) Angle \( ABC \) is a corner of the rectangle, and every corner of a rectangle is exactly \( 90^\circ \), which is called a right angle. [B1]

(b) Opposite sides of a rectangle are equal, so \( AB = DC = 12 \) cm and \( BC = AD = 9 \) cm:

(c) The diagonal \( AC \) is the hypotenuse of the right-angled triangle \( ABC \), whose shorter sides are \( AB = 12 \) cm and \( BC = 9 \) cm. By Pythagoras' theorem:

(d) Turning the rectangle through \( 180^\circ \) about its centre maps it exactly onto itself, and a further \( 180^\circ \) returns it to the start, so it fits onto itself twice in a full turn. The order of rotational symmetry is \( 2 \). [B1]

The right angle at \( B \) is what makes Pythagoras' theorem available in part (c), and \( 9 \), \( 12 \), \( 15 \) is the \( 3 \), \( 4 \), \( 5 \) triple multiplied by \( 3 \). Note that a rectangle has only \( 2 \) lines of symmetry and rotational symmetry of order \( 2 \), whereas a square has \( 4 \) of each; the diagonals of a rectangle are not lines of symmetry.