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Congruence

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Aadhyaan Tiwari

1. The document discusses different postulates for proving triangle congruence, including SSS, SAS, ASA, AAS, RHS, and hypothetical cases like SSA and AAA. 2. It warns that there is no actual SSA or AAA postulate to prove congruence and provides examples of non-congruent triangles that satisfy SSA or AAA. 3. The key postulates listed are SSS, SAS, ASA, AAS, and RHS, with RHS only applying to right triangles.

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Filp Model ...............................................Class IXFFlliipp MMooddeell--CCllaassss IIXX1
TThhee IIddeeaa ooff CCoonnggrruueennccee Two geometric figures with exactly the same size and shape. B A C F E D Filp Model ...............................................Class IX 2
CCoorrrreessppoonnddiinngg PPaarrttss Recap: If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C DABC @ D DEF E D F 1. AB @ DE 2. BC @ EF 3. AC @ DF 4. A @ D 5. B @ E 6. C @ F Filp Model ...............................................Class IX 3
HHooww mmuucchh ddoo yyoouu nneeeedd ttoo kknnooww.. .. .. . . . about two triangles to prove that they are congruent? Filp Model ...............................................Class IX 4
SSSSSS IIff wwee ccaann sshhooww aallll 33 ppaaiirrss ooff ccoorrrr.. ssiiddeess aarree ccoonnggrruueenntt,, tthhee ttrriiaanngglleess hhaavvee ttoo bbee ccoonnggrruueenntt.. Filp Model ...............................................Class IX 5
SSAASS SShhooww 22 ppaaiirrss ooff ssiiddeess aanndd tthhee iinncclluuddeedd aanngglleess aarree ccoonnggrruueenntt aanndd tthhee ttrriiaanngglleess hhaavvee ttoo bbee ccoonnggrruueenntt.. IInncclluuddeedd aannggllee NNoonn--iinncclluuddeedd aanngglleess Filp Model ...............................................Class IX 6
AASSAA aanndd AAAASS AASSAA 22 aanngglleess aanndd tthhee iinncclluuddeedd ssiiddee AA SS AA AAAASS 22 aanngglleess aanndd TThhee nnoonn--iinncclluuddeedd ssiiddee AA AA SS Filp Model ...............................................Class IX 7
RRHHSS (( hhyyppootteennuussee lleegg )) iiss uusseedd oonnllyy wwiitthh rriigghhtt ttrriiaanngglleess,, BBUUTT,, nnoott aallll rriigghhtt ttrriiaanngglleess.. RRHHSS AASSAA Filp Model ...............................................Class IX 8
WWaarrnniinngg:: NNoo SSSSAA PPoossttuullaattee B There is no such thing as an SSA postulate! A C E D F NOT CONGRUENT Filp Model ...............................................Class IX 9
WWaarrnniinngg:: NNoo AAAAAA PPoossttuullaattee B A C E D F There is no such thing as an AAA postulate! NOT CONGRUENT Filp Model ...............................................Class IX 10
TThhee CCoonnggrruueennccee PPoossttuullaatteess SSS correspondence ASA correspondence SAS correspondence AAS correspondence RHS correspondence SSA correspondence AAA correspondence Filp Model ...............................................Class IX 11
NNaammee tthhee PPoossttuullaattee ((II)) (when possible) SSAASS AASSAA SSSSAA SSSSSS Filp Model ...............................................Class IX 12
NNaammee tthhee PPoossttuullaattee (when possible) AASSAA AAAAAA SSAASS SSSSAA Filp Model ...............................................Class IX 13
NNaammee tthhee PPoossttuullaattee ((IIII)) (when possible) Reflexive SSAASS SSAASS SSAASS Property Vertical Angles Vertical Angles Reflexive Property SSSSAA Filp Model ...............................................Class IX 14
NNaammee tthhee PPoossttuullaattee ((IIIIII)) (when possible) Filp Model ...............................................Class IX 15
(when NNaammee tthhee PPoossttuullaattee ((IIVV po))ssible) Filp Model ...............................................Class IX 16

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Congruence

  • 1. Filp Model ...............................................Class IXFFlliipp MMooddeell--CCllaassss IIXX1
  • 2. TThhee IIddeeaa ooff CCoonnggrruueennccee Two geometric figures with exactly the same size and shape. B A C F E D Filp Model ...............................................Class IX 2
  • 3. CCoorrrreessppoonnddiinngg PPaarrttss Recap: If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C DABC @ D DEF E D F 1. AB @ DE 2. BC @ EF 3. AC @ DF 4. A @ D 5. B @ E 6. C @ F Filp Model ...............................................Class IX 3
  • 4. HHooww mmuucchh ddoo yyoouu nneeeedd ttoo kknnooww.. .. .. . . . about two triangles to prove that they are congruent? Filp Model ...............................................Class IX 4
  • 5. SSSSSS IIff wwee ccaann sshhooww aallll 33 ppaaiirrss ooff ccoorrrr.. ssiiddeess aarree ccoonnggrruueenntt,, tthhee ttrriiaanngglleess hhaavvee ttoo bbee ccoonnggrruueenntt.. Filp Model ...............................................Class IX 5
  • 6. SSAASS SShhooww 22 ppaaiirrss ooff ssiiddeess aanndd tthhee iinncclluuddeedd aanngglleess aarree ccoonnggrruueenntt aanndd tthhee ttrriiaanngglleess hhaavvee ttoo bbee ccoonnggrruueenntt.. IInncclluuddeedd aannggllee NNoonn--iinncclluuddeedd aanngglleess Filp Model ...............................................Class IX 6
  • 7. AASSAA aanndd AAAASS AASSAA 22 aanngglleess aanndd tthhee iinncclluuddeedd ssiiddee AA SS AA AAAASS 22 aanngglleess aanndd TThhee nnoonn--iinncclluuddeedd ssiiddee AA AA SS Filp Model ...............................................Class IX 7
  • 8. RRHHSS (( hhyyppootteennuussee lleegg )) iiss uusseedd oonnllyy wwiitthh rriigghhtt ttrriiaanngglleess,, BBUUTT,, nnoott aallll rriigghhtt ttrriiaanngglleess.. RRHHSS AASSAA Filp Model ...............................................Class IX 8
  • 9. WWaarrnniinngg:: NNoo SSSSAA PPoossttuullaattee B There is no such thing as an SSA postulate! A C E D F NOT CONGRUENT Filp Model ...............................................Class IX 9
  • 10. WWaarrnniinngg:: NNoo AAAAAA PPoossttuullaattee B A C E D F There is no such thing as an AAA postulate! NOT CONGRUENT Filp Model ...............................................Class IX 10
  • 11. TThhee CCoonnggrruueennccee PPoossttuullaatteess SSS correspondence ASA correspondence SAS correspondence AAS correspondence RHS correspondence SSA correspondence AAA correspondence Filp Model ...............................................Class IX 11
  • 12. NNaammee tthhee PPoossttuullaattee ((II)) (when possible) SSAASS AASSAA SSSSAA SSSSSS Filp Model ...............................................Class IX 12
  • 13. NNaammee tthhee PPoossttuullaattee (when possible) AASSAA AAAAAA SSAASS SSSSAA Filp Model ...............................................Class IX 13
  • 14. NNaammee tthhee PPoossttuullaattee ((IIII)) (when possible) Reflexive SSAASS SSAASS SSAASS Property Vertical Angles Vertical Angles Reflexive Property SSSSAA Filp Model ...............................................Class IX 14
  • 15. NNaammee tthhee PPoossttuullaattee ((IIIIII)) (when possible) Filp Model ...............................................Class IX 15
  • 16. (when NNaammee tthhee PPoossttuullaattee ((IIVV po))ssible) Filp Model ...............................................Class IX 16