Page 26 - Mathematics_Form_Two

Congruence

Postulate 3. State the argument which needs to be
A postulate is a statement that is accepted proved.
as true without any proof. These statements 4. Where necessary, make additional
are universally accepted, self-evident and constructions with dotted lines to
can form the basis for further reasoning make the proof clear.
and making arguments. The following are 5. In writing the proof;
FOR ONLINE READING ONLY
examples of postulates. (i) Refer the figures you have
Mathematics for Secondary Schools (ii) A straight line can be drawn from (ii) Provide arguments with reasons
(i) A circle can be drawn with any
planned to use in the proof.
centre and radius.
based on the given information or
any point to any other point.
established facts.
(iii) All right angles are equal to each
(iii) Start with statements whose
other.
validity are given or are obvious.
Theorem
conclusion about what was
A theorem is an argument that has been (iv) The final statement is the
supposed to be proved.
proved to be true based on past established
results, definitions or postulates. The Engage in Activity 2.2 to explore more
following are examples of theorems. about postulates, proofs, and theorems.
(i) The sum of interior angles of a Activity 2�2: Exploring postulates,
triangle is 180 degrees. proofs, and theorems
(ii) In a right-angled triangle, the square Identify a list of postulates, proofs, and
of the length of the hypotenuse is theorems from reliable sources and
equal to the sum of the squares of the briefly explain why each is accepted as
lengths of the other two sides. a postulate, proof or theorem.
(iii) The sum of interior angles of a
quadrilateral is 360 degrees.
Example 2�1
Proof Prove that the sum of interior angles of
A proof is a series of logical statements a triangle is 180°.
that are based on definitions, previously
established facts, and postulates that Solution
may be used to conclude the truth of a Consider the triangle ABC as shown in
mathematical argument. The following
are common procedures when undertaking the following figure.
a proof.
1. Draw a clearly labelled diagram to
represent a problem. Indicate all the
information such as equal angles,
parallel lines, and congruent segments.
2. Write down the given information
based on the labels of the supporting Required to prove that,
figures. CAB BCA ABC 180 .+ ˆ ˆ + ˆ = °

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 20 11/10/2024 20:11:12