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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