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Congruent Triangles

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. CONGRUENCE CONDITIONS.

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Congruent Triangles

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  1. Congruent Triangles Part II Class VII

  2. 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

  3. 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. 

  4. 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 )

  5. SSS SAS ASA RHS 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. ONE SET OF EQUAL SIDES ANOTHER SET OF EQUAL SIDES THIRD SET OF EQUAL SIDES FORM CONGRUENT TRIANGLES SSS CONGRUENCE CONDITION

  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 S A S 1 2

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

  11. FOR THE GIVEN PAIR OF SIDES FIND THE INCLUDED ANGLE Write the answers in the note book, click next slide for checking. • Sides PR & PQ • Sides RS &PS • Sides PQ & PS • Sides RS & RQ • Sides SO &PO S R O P Q

  12. CHECK THE ANSWERS • RPQ • PSR • SPQ • SRQ • 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 A SIDE(PINK) THEY ARE NOT CONGRUENT!!! Another side (GREEN) With the same measurement ,Another  1 ONE  One Angle but not included

  15. try ASA CONGRUENCY

  16. RHS CONGRUENT CONDITION RRight angle Hhypotenuse Sany side other than hypotenuse

  17. RHS CONGRUENCE CONDITION 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

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