Page 52 - MAT KS3 Y8 Cambridge CheckPoint

5 Angles

Do you remember that the angles of a triangle add up to 180 °?
Key words
How did you find out that this is true? Make sure you learn and
understand these key words:
Did you draw a triangle, tear off the corners and put them together
parallel
to make a straight line?
transversal
corresponding angles
alternate angles
C
prove
proof
external angle
A B B C A

Did you use a protractor to measure the three angles of a triangle, then add them together
to get a total close to 180 °?
These methods show that the result is reasonable. They do not prove it is true for any triangle.

A proof is a logical argument in which each step is explained or justified by a reason.

Over 2000 years ago the Greek mathematician Euclid wrote a book called The Elements.
He tried to use logical arguments to prove many facts in geometry and arithmetic.
His book was the most successful textbook ever written. It is still in print today.

Euclid started with definitions of basic things such as a point and a
straight line. He also had a set of statements which he thought
everyone could agree with. These were called axioms.
An example of one of his axioms is:
r Things that are equal to the same thing are equal to one another.

From this simple starting point he proved many complicated results.

In this unit you will learn to understand several proofs. You will also solve geometrical problems and
explain your reasons.

50 5 Angles