Congruent Triangles
Part IIClass VII
CONGRUENCE CONDITIONS
IF THREE SIDES AND THREE ANGLES OF
ONE ARE EQUAL TO THREE SIDES AND
THREE ANGLES OF ANOTHER
(total six sets)
A TRIANGLE
IS CONGRUENT TO
ANOTHER TRIANGLE
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 )
CONGRUENCE CONDITIONS
SSSSSS
SASSAS
ASAASA
RHSRHSLET US LEARN ABOUT
THIS HERE
SSS CONGRUENCE CONDITION
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
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
12
S
A
S
INCLUDED ANGLES
FOR SIDE (GREEN) & SIDE (PINK)
“ 1 ” IS THE INCLUDED ANGLE.
12
FOR SIDE (PINK) &SIDE (YELLOW) “ 2 ” IS THE INCLUDED ANGLE
FOR THE GIVEN PAIR OF SIDES FIND THE INCLUDED
ANGLE
P Q
RS
1. Sides PR & PQ
2. Sides RS &PS
3. Sides PQ & PS
4. Sides RS & RQ
5. Sides SO &PO
O
Write the answers in the note book, click next slide for checking.
CHECK THE ANSWERS
1. RPQ
2. PSR
3. SPQ
4. SRQ
5. SOP
REMEMBERIN ‘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
1
A SIDE (PINK)
Another side
(GREEN)
One Angle but not includedONE
With the same measurement ,Another
THEY ARE NOT CONGRUENT!!!
RHS CONGRUENT CONDITION
R Right angle
H hypotenuse
S 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
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