G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

 

Year 10 Interactive Maths - Second Edition


Basic Geometry

Geometry is used in surveying, navigation, astronomy and many practical occupations. Astronomers use geometry to measure the distance from the Earth to other planets, and chemists use it to comprehend the structure of molecules. Geometrical drawings are widely used by surveyors, architects and engineers. Navigation by sea and by air depends on accurate geometry.

In this chapter we will revise the angle facts of geometry, the main features of triangles and quadrilaterals; and their use in solving numerical problems.


Angle Facts of Geometry

You should be familiar with the following angle facts of geometry:

Complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees and the sum of adjacent angles forming a straight line is 180 degrees (i.e. u + v = 180 degrees).

Two angles of size v degrees and u degrees are adjacent angles forming a straight line.

The sum of all angles meeting at a point is 360 degrees (i.e. a + b + c = 360).

Three angles of size a degrees, b degrees and c degrees meet at a point.  Their sum is 360 degrees.


If two parallel lines are cut by a transversal, then:  (a)  z = x (or u = v).  z and x (or u and v) are known as alternate angles.  (b)  x = y.  x and y are known as corresponding angles.  (c)  y = z.  y and z are known as vertically opposite angles.  (d)  u + x = 180.  u and x are known as allied (or co-interior) angles and are supplementary.

A transversal cuts two parallel lines with angles of size v degrees, x degrees, z degrees, u degrees and y degrees indicated.


Example 1

Find the value of the pronumeral(s) in each of the following diagrams:

a.

Two angles of size x degrees and 40 degrees form a straight line.

b.

Three angles of size 152 degrees, a degrees and 120 degrees meet at a point.

c.

A transversal cuts two parallel lines and four angles of size x degrees, 70 degrees, y degrees and 2z degrees are marked.

Solution:

(a)  x + 40 = 180     {Sum of adjacent angles}.  Subtract 40 from both sides to find x = 140.

(b)  a + 152 + 120 = 360     {Sum of angles at a point}.  Subtract 272 from both sides to find a = 88.

(c)  x = 70     {Vertically Opposite Angles}.  y = 70     {Alternate angles}.  2z = 70 and so z = 35     {Corresponding angles}.


Key Terms

geometry, angle facts of geometry, complementary angles, supplementary angles, adjacent angles forming a straight line, angles at a point, parallel lines, transversal, alternate angles, corresponding angles, vertically opposite angles, allied angles, co-interior angles

 

Study Another Topic in Chapter 6: Geometry

[ Basic Geometry ] Triangles ] Deductive Geometry ] Congruence ] Similar Figures ] Quadrilaterals ] Tangent to a Circle ] Circle Terminology ] Segments of a Circle ] Concyclic Points ] Problem Solving Unit ] Projects ] Symbols ] Index ]

 

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