Congruent Triangles Part II Class VII. CONGRUENCE CONDITIONS I F THREE SIDES AND THREE ANGLES OF ONE  ARE EQUAL TO THREE SIDES AND THREE ANGLES OF ANOTHER.

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Presentation transcript:

Congruent Triangles Part II Class VII

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

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

SSSSASASARHS LET 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 S IDES ANOTHER SET OF EQUAL S IDES THIRD SET OF EQUAL S IDES 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. 1 2 FOR SIDE (PINK) &SIDE (YELLOW) “ 2 ” IS THE INCLUDED ANGLE

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.

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 1 A SIDE (PINK) Another side (GREEN) One Angle but not included ONE  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