Transcript Congruent Triangles

Congruent
Triangles
Part II
Class VII
CONGRUENCE CONDITIONS

A TRIANGLE
IS CONGRUENT TO
ANOTHER
TRIANGLE
IF THREE SIDES AND
THREE ANGLES OF
ONE  ARE EQUAL TO
THREE SIDES AND
THREE ANGLES OF
ANOTHER 
(total six sets)
CONGRUENCE CONDITIONS

BUT WITH ONLY THREE SETS OF
EQUALITIES ( INSTEAD OF SIX SETS OF
EQUALITIES) THE TWO TRIANGLES WILL
PROVED TO BE CONGRUENT. THAT IS
THE OTHER THREE SETS ARE FOUND TO
BE EQUAL AUTOMATICALLY.
CONGRUENCE CONDITIONS
THE THREE SETS OF EQUALITIES ARE
*SSS ( THREE SIDES OF TWO s )
*ASA ( TWO ANGLES AND THE
INCLUDED SIDE OF TWO s )
*SAS (TWO SIDES AND THE INCLUDED
ANGLE OF TWO s )
*RHS ( HYPOTENUSE, A SIDE OF TWO
RIGHT ANGLED s )
SSS
SAS
LET US
LEARN
ABOUT
THIS HERE
ASA
RHS
Two Triangles are
congruent if
THREE sides
of one triangle are
respectively equal to the
THREE sides
of the other triangle
SSS CONGRUENCE CONDITION
ONE SET OF EQUAL SIDES
ANOTHER SET OF EQUAL SIDES
THIRD SET OF EQUAL SIDES
FORM CONGRUENT
TRIANGLES
SSS CONGRUENCE CONDITION
Side –Angle – Side (SAS)
Congruence Condition
Two Triangles are congruent if
two sides and the included
angle of one triangle are
respectively equal to the two
sides and the included angle of
the other triangle
Side –Angle – Side (SAS)
Condition
S
A
S
12
INCLUDED ANGLES
SIDE
(GREEN)
SIDE (PINK)
FORFOR
SIDE
(PINK)
&SIDE&(YELLOW)
“ 2 ” IS
INCLUDED
ANGLE ANGLE.
“ 1THE
” IS
THE INCLUDED
2
1
FOR THE GIVEN PAIR OF
SIDES FIND THE INCLUDED
the answers in
ANGLE Write
the note book, click
next slide for
checking.
1. Sides
PR & PQ
2. Sides
RS &PS
S
R
3. Sides
PQ & PS
O
4. Sides
RS & RQ
5. Sides
SO &PO
P
Q
CHECK THE ANSWERS
1. RPQ
2. PSR
3. SPQ
4. SRQ
5. SOP
REMEMBER
IN ‘SAS’ CONDITION THE
ANGLE MUST BE AN
INCLUDED ANGLE .
THE TRIANGLES NEED NOT
BE CONGRUENT IF THE
ANGLES ARE NOT
“INCLUDED”
Side –Angle – Side (SAS)
Condition
A SIDE
(PINK)
THEY ARE NOT
CONGRUENT!!!
Another side
(GREEN)
1
ONE 
With the same
measurement
,Another 
One Angle but not included
RHS CONGRUENT
CONDITION
R
H
S
Right angle
hypotenuse
any side other than
hypotenuse
Two RIGHT Triangles are
congruent if
HYPOTENUSE &
ONE SIDE
of one triangle are
respectively equal to the
HYPOTENUSE &
ONE SIDE
of the other
RIGHT Triangle
RHS CONGRUENCE CONDITION