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SIMILARITY AND
CONGRUENCY
BASIC COMPETENCE :

1.2. TO IDENTIFY THE PROPERTIES OF TWO
SIMILAR AND CONGRUENT TRIANGELS
INDICATOR :



TO DETERMINE REQUIREMENTS FOR
TWO SIMILAR TRIANGLES
TO DETERMINE THE RATIO OF THE
SIDES OF TWO TRIANGLES AND
FINDING THE SIDE LENGTHS
TO DETERMINE REQUIREMENTS FOR
TWO CONGRUENT TRIANGLES
LOOK AT THE FIGURE BELOW
A
AB is the height of building
BC is the length of image of building
C
B
K
KL is the length of flag pole
LM is the length of image of flag pole
L
M
LM
BC
A

THE CORRESPONDING ANGELS OF BOTH
TRIANGLES ARE :
 B =  L = 900
C
50 m
AND  A =  K

30 m
B
SO THE CORRESPONDING
ANGELS ARE THE SAME SIZE
C
THE CORRESPONDING SIDES OF BOTH
TRIANGLES ARE :
K

5m
3m
L
=M= 

M
LM
BC
KL
AB
=
3
30
=
=
5
50
=
1
10
1
10
FROM THE EXPLAINATION ABOVE WE CAN
SAY THAT :
THE CORRESPONDING ANGLES ARE THE
SAME SIZE.
2.
THE RATIO OF CORRESPONDING SIDES
ARE EQUAL.
SO, WE CAN SAY THAT TWO TRIANGLES
ABOVE ARE SIMILARY.
1.

SO, THE PROPERTIES FOR THE
SIMILARITY OF TWO TRIANGLES ARE
AS FOLLOWS :
1. THE CORRESPONDING ANGLES ARE
THE SAME SIZE.
2. THE RATIO OF CORRESPONDING
SIDES ARE EQUAL
LOOK AT THE FIGURE BELOW
A
K
B
C
L
P
Q
R
M


IF  ABC MOVES TO THE RIGHT SO
EXACTLY COVERS TO  KLM, SO WE
CAN SAY THAT  ABC AND  KLM ARE
CONGRUENT.
IF TWO TRIANGLES ARE CONGRUENT IT
MUST BE SIMILAR. IF TWO TRIANGLES
ARE SIMILAR IT MUST NOT BE
CONGRUENT.
LOOK AT THE FIGURE BELOW :
A
B
K
C L
AB = KL
 ABC AND  KLM ARE CONGRUENT
BC = LM
BASED ON ( SIDE , SIDE , SIDE )
AC = KM
M
A
K
C L
B
AB = KL
SO,  ABC AND  KLM ARE CONGRUENT
B=L
BASED ON ( SIDE , ANGLE , SIDE )
BC = LM
M
A
K



C L
B
B=L
 ABC AND  KLM ARE CONGRUENT
BC = LM
BASED ON ( ANGLE , SIDE , ANGLE )
C=M

M
CONCLUSION :

TWO TRIANGLES ARE CALLED SIMILAR IF :





THE CORRESPONDING ANGLES ARE THE SAME
SIZE.
THE RATIO OF THE CORRESPONDING SIDES ARE
EQUAL.
TWO TRIANGLES ARE CALLED CONGRUENT IF :
1. THE CORRESPONDING SIDES ARE THE SAME
SIZE.( SIDE , SIDE , SIDE )
2. IF THE SIZE OF ONE ANGLE OF TWO TRIANGLES
ARE THE SAME AND IT LIES BETWEEN TWO
RESPECTIVE SIDES OF THE SAME LENGTH (SIDE ,
ANGLE , SIDE )
TWO TRIANGLES ARE CALLED CONGRUENT IF :



1. THE CORRESPONDING SIDES ARE THE SAME SIZE.(
SIDE , SIDE , SIDE )
2. IF THE SIZE OF ONE ANGLE OF TWO TRIANGLES
ARE THE SAME AND IT LIES BETWEEN TWO
RESPECTIVE SIDES OF THE SAME LENGTH (SIDE ,
ANGLE , SIDE )
3. IF THE LENGTH OF ONE SIDE OF TWO TRIANGLES
ARE THE SAME AND IT LIES BETWEEN TWO
RESPECTIVE ANGLES WITH THE SAME SIZE ( ANGLE ,
SIDE , ANGLE )