23A Core skills 1. Copy and complete the table showing properties of quadrilaterals, using Y for yes or N for no. Square Rectangle Parallelogram Rhombus
Diagonals of equal length Four sides of equal length Four equal angles Exactly two pairs of parallel sides Two pairs of equal sides (but not all equal) Diagonals that bisect each other Two pairs of equal angles (but not all equal)
2. (i) Construct a rectangle PQRS, where |PQ| = 110 mm, |QR| = 5·5 cm (ii) Find the perimeter and the area of this rectangle.
3. A rectangle has a perimeter of 0 · 8 m and a width of 10 cm. Find its length. 4. A square has a perimeter of 12 · 4 cm. Find the length of a side of the square.
5. Find the perimeter and the area of each of the following shapes. (i)
25 cm (ii) 7 cm (iii) 2 m 4 cm 7 cm 4 m
6. Find the measure of angles labelled A to D and the sides m and n in the following diagrams. Justify your answer by giving the theorem or axiom used to fi nd each answer.
(i) D 10mm 66° m A 20 mm 114° B n C m B 43 cm C (ii) A n D 23 cm 120° (iii) m 97° C 10 m B 5.5 m
7. Find the value of x and y in each of the following diagrams. Justify your answer by giving the theorem or axiom used to fi nd each answer.
(i) 2x 40 4y 22 (ii) 2x + 6
3y + 14 74 107
(iii)
2 11x + 22 133
y 161 D A n 6 m 2 m Remember: all
dimensions should have the same units before area and perimeter are calculated.
(iv)
1 m
1 m
8. Write down whether the object in each of the following has been transformed by refl ection, rotation or translation. Justify your answer in each case.
(i) J (ii) Q (iii) G G Section B Moving forward 387