1. Congruent Triangles Part II Class VII

2. CONGRUENCE CONDITIONS I F 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

3. 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 

4. 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

5. SSSSASASARHS LET US LEARN ABOUT THIS HERE

6. SSS CONGRUENCE CONDITION Two Triangles are congruent if THREE sides of one triangle are respectively equal to the THREE sides of the other triangle

7. SSS CONGRUENCE CONDITION ONE SET OF EQUAL S IDES ANOTHER SET OF EQUAL S IDES THIRD SET OF EQUAL S IDES FORM CONGRUENT TRIANGLES

8. 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

9. Side –Angle – Side (SAS) Condition 12 S A S

10. INCLUDED ANGLES FOR SIDE (GREEN) & SIDE (PINK) “ 1 ” IS THE INCLUDED ANGLE. 1 2 FOR SIDE (PINK) &SIDE (YELLOW) “ 2 ” IS THE INCLUDED ANGLE

11. FOR THE GIVEN PAIR OF SIDES FIND THE INCLUDED ANGLE PQ R S 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.

12. CHECK THE ANSWERS 1.  RPQ 2.  PSR 3.  SPQ 4.  SRQ 5.  SOP

13. REMEMBER  IN ‘SAS’ CONDITION THE ANGLE MUST BE AN INCLUDED ANGLE.  THE TRIANGLES NEED NOT BE CONGRUENT IF THE ANGLES ARE NOT “INCLUDED”

14. Side –Angle – Side (SAS) Condition 1 A SIDE (PINK) Another side (GREEN) One Angle but not included ONE  With the same measurement,Another  THEY ARE NOT CONGRUENT!!!

16. RHS CONGRUENT CONDITION R Right angle H hypotenuse S any side other than hypotenuse

17. 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