TYPE OF QUADRILATERAL

• A quadrilateral is two-dimensional shape with four side and four angles.

• A quadrilateral with both pairs of opposite sides parallel is called a parallelogram. A parallelogram has two pairs of equal

sides.

• There are three special types of parallelogram

Question

• Name the quadrilateral that remains when the two equal right-angled triangles (shaded) are cut off this rectangle.

Solution

• The quadrilateral that remains has just one pair of parallel sides and

• so is not a parallelogram. • It is a trapezium. • Because the non-parallel sides are equal, it is an isosceles trapezium.

Question 1

• Name each of the following quadrilaterals:

Solution

a rectangle b trapeziumc kite d squaree rhombus f parallelogramg trapezium h quadrilateral

Question 2

• Name each of the quadrilaterals described in this table.

Solution

a square b trapeziumc rhombus d quadrilateral

Question Only part of the complete description is given for

each of the following quadrilaterals. List all of the quadrilaterals that could be described in each of these ways.

a A quadrilateral that has four equal sides.b A quadrilateral that has two pairs of equal sides.c A quadrilateral that has two pairs of parallel

sides.d A quadrilateral that has one pair of parallel sides

and one pair of equal sides.

Solution

a square, rhombusb rectangle, parallelogram, kitec rectangle, parallelogram, square, rhombusd isosceles trapezium

Question On a sheet of grid paper plot each of these sets of points,

and name the quadrilateral formed each time.

a ABCD where A (1, 2), B (3, 6), C (9, 6) and D (7, 2)b XYZW where X (0, 0), Y (1, 6), Z (4, 7) and W (3, 1)c MNOP where M (1, 1), N (3, 6), P (7, 6) and Q (9, 1)d RSTU where R (1, 5), S (4, 0), T (7, 5) and U (4, 10)e EFGH where E (0, 5), F (3, 7), G (6, 5) and H (3, 1)

Solution

The angle sums of quadrilaterals The four angles inside a quadrilateral add

up to 360°. Again this can be shown by putting the vertices of the angles together.

Question

• Find the size of m° in this figure.

Solution

The angle sum of a quadrilateral is 360°.So:m° + 90° + 120° + 80° = 360°m° + 290° = 360°m° = 70°

Question

• Without using a protractor, find the sizes of the marked angles in each of the following shapes:

Solution

a x° = 30°, y° = 35°, z° = 105°b x° = 30°, y° = 115°, z°= 65°c x° =y° = 65°, z°= 25°d x° = 75°, y° = 105°e x° = y° = z° = w°= 45°f x° = y° = z° = 60°

Question

• find the sizes of the marked angles in each of the following shapes.

Solution

a x° = 55°, y°= 70°b x°= 80°, y° = 80°c x° = 50°, y° = 55°, z° = 40°d x° = 35°, y° = 50°, z°= 25°, w° = 155°