Page 40 - Mathematics_Form_Two

Congruence

10. In the following figure, D is of two corresponding sides
the midpoint of BC, X and and the included angle of other
Y are points on AB and triangle (SAS).
respectively. If DX = DY and (c) (i) Two angles and the included
ˆ
ˆ
DYC =
DXB = ACD. 90 .° Prove that side of one triangle are
respectively equal to the
FOR ONLINE READING ONLY
ˆ
ˆ
ABD =
Mathematics for Secondary Schools (ii) Two angles and non-included
corresponding two angles
and the included side of the
other triangle (ASA).
side of one triangle are
respectively equal to the
corresponding two angles
and a non-included side of
the other triangle (AAS).
Chapter summary 6. Two right-angled triangles are
1. Two figures are said to be congruent congruent if their hypotenuses and a
if they have exactly the same size and pair of sides have equal length.
shape.
2. A postulate a statement that is Revision exercise 2
accepted without any proof. 1. In the following figure, BA = BC

3. A theorem is an argument that has and KA = KC. Prove that
been proven to be true based on past BAK = BCK.
ˆ
ˆ
established results or definitions or
postulates.
4. A proof is a series of logical
statements that are based on
definitions, previously established
facts, and postulates that may be used
to conclude the truth of mathematical
arguments.
5. Two triangles are congruent if: 2. A quadrilateral MNOP has

(a) The sides of one triangle have the property that MN = OP
equal lengths to the corresponding and MP = NO. Prove that
ˆ
ˆ
sides of the other triangle (SSS). PMN = NOP.
(b) The lengths of two sides and the
included angle of one triangle are 3. Use the following figure to prove
respectively equal to the lengths that ML = PL.

34
Student's Book Form Two

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