Lines, angles and

polygons

4

Contents:

A Angle properties [4.4]

B Triangles [4.4]

C Isosceles triangles [4.4]

D The interior angles of a polygon [4.4]

E The exterior angles of a polygon [4.4]

Opening problem

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On his birthday, Billy receives a cake in the shape of a regular

hexagon. He divides the cake into 4 pieces by making cuts from

one corner to each of the other corners as shown.

Things to think about:

a When Billy cuts the cake in this way, are the four angles

at the top of the hexagon equal in size? Can you find the

size of each angle?

b When a regular hexagon is cut in this way, four triangles

are formed. Do any of these triangles contain right angles?

There is some important terminology we use when talking about how two angles are related. You should

become familiar with these terms:

² Two angles with sizes which add to 90 oare calledcomplementary angles.

² Two angles with sizes which add to 180 oare calledsupplementary angles.

A ANGLE PROPERTIES [4.4]

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Y:\HAESE\IGCSE01\IG01_04\093IGCSE01_04.CDR Tuesday, 4 November 2008 12:05:41 PM PETER