Page 91 - MAT KS3 Y8 Cambridge CheckPoint

8.3 Classifying quadrilaterals

Worked example 8.3

I am a quadrilateral with no lines of symmetry.
My diagonals cross, but not at 90°, and they do not bisect each other.
What shape am I?

Trapezium No lines of symmetry means the shape could be a parallelogram or a trapezium. The diagonals don’t
bisect each other means it is a trapezium.
✦ Exercise 8.3

1 Name each special quadrilateral being described.
a All my sides are the same length. My diagonals bisect each other at 90°. I have 4 lines of symmetry.
b I have order 2 rotational symmetry, but no lines of symmetry.
c I have two pairs of equal sides, but only one pair of equal angles.
d I have diagonals that bisect each other, but not at 90°.
e I have one pair of parallel sides. I have order 1 rotational symmetry. I also have one line of
symmetry.
2 Check each quadrilateral against this classification flow chart.
Write down the letter where each shape comes out.
a square
b rhombus
c kite Start
d parallelogram
e trapezium
Yes Diagonals bisect No
f isosceles trapezium
each other
g rectangle

Yes No
Diagonals cross at 90º
Yes Diagonals bisect No
each other at 90º M
Yes No
1 line of symmetry
Yes No Yes No
Rotational symmetry 2 lines of symmetry
order 2 N P

H J K L

3 Plot these points on a coordinate grid.
A(2, 5), B(4, 5), C(4, 3), D(2, 3), E(1, 3), F(3, 5), G(7, 3), H(3, 1), I(5, 3), J(7, 1)
Join up points to make the following shapes.
Write down the coordinates of the point where the diagonals cross.
a ABCD b EFGH c EIJH

8 Shapes and geometric reasoning 89