Congruence and Similarity (II) 9.31
In the figure, PQRS , FGHK. Find x and y.
5
R
S P Q
y
38°
42°
G
F
K
H
x
a PQRS , FGHK
` FG = PQ
x = 5
+GFK = +QPS
= y
In 3FGK,
+FGK ++FKG + +GFK = 180c (+ sum of 3)
42c + 38c + y = 180c
y = 100c
Level 1
Example 13
Solution
Diagram Clue
38°
5
42°
GR
S P Q
F
K
H
x
y
Corresponding sides
are equal.
◀ Corresponding angles
are equal.
◀
We learnt that in two congruent figures, their corresponding angles are
equal and their corresponding sides are equal. Obviously, if two figures
have all these properties, then they are congruent. However, if two
figures do not have any of these properties, then they are not congruent.
Some examples are illustrated below.
e.g. (a) Each pair of the figures below does not have the property
'corresponding angles are equal'. They are not congruent.
(i) (ii)
80° 85°
130° 125° 133°
135°
100° 104°
95° 93°
E
F I T
Q
P
H R S
G
110° 110°
130° 135°
50° 50°
70° 65°
A P
R
B D Q S
C
+E is not equal to any angle of PQRST. +A = +P and +B = +Q,
but +C !+R and +D !+S.
In the figure, ABCD , EFGH. Find x, y and z.
60°
6 D C
B
A
y
7
H
E
F
G
z x
13
Instant Drill
➥ Ex 9C 5