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4.3-5 Triangle Congruence

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- SSS, SAS, AAS, ASA, HL
- Unsing Triangle Congruence Properties

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4.3-5 Triangle Congruence

  1. 1. Sections 4-3 - 4-5
  2. 2. When we talk about congruent triangles,we mean everything about them is congruent.All 3 pairs of corresponding angles are equal….And all 3 pairs of corresponding sides are equal
  3. 3. For us to prove that 2 people areidentical twins, we don’t need to showthat all “2000” body parts are equal. Wecan take a short cut and show 3 or 4things are equal such as their face, ageand height. If these are the same I thinkwe can agree they are twins. The sameis true for triangles. We don’t need toprove all 6 corresponding parts arecongruent. We have 5 shortcuts or methods.
  4. 4. SSS If we can show all 3 pairs of corr.sides are congruent, the triangles have to be congruent.
  5. 5. SAS Show 2 pairs of sides and theincluded angles are congruent andthe triangles have to be congruent. Non-included angles Included angle
  6. 6. This is called a common side.It is a side for both triangles.We’ll use the reflexive property.
  7. 7. Which method can be used toprove the triangles are congruent
  8. 8. Common side SSS Vertical angles SASParallel linesalt int anglesCommon side SAS
  9. 9. ASA, AAS and HL AASA – 2 anglesand the included side S AAAS – 2 angles andThe non-included side A A S
  10. 10. HL ( hypotenuse leg ) is usedonly with right triangles, BUT, not all right triangles. HL ASA
  11. 11. When Starting A Proof, Make The Marks On The Diagram IndicatingThe Congruent Parts. Use The Given Info, Properties, Definitions, Etc.We’ll Call Any Given Info That DoesNot Specifically State Congruency Or Equality A PREREQUISITE
  12. 12. SOME REASONS WE’LL BE USING• DEF OF MIDPOINT• DEF OF A BISECTOR• VERT ANGLES ARE CONGRUENT• DEF OF PERPENDICULAR BISECTOR• REFLEXIVE PROPERTY (COMMON SIDE)• PARALLEL LINES ….. ALT INT ANGLES
  13. 13. Given: AB = BDA C EB = BC B ˜ Prove: ∆ABE = ∆DBC 1 2 Our Outline P rerequisitesE SAS D S ide A ngle S ide Triangles = ˜
  14. 14. A C Given: AB = BD B EB = BC 1 2 ˜ Prove: ∆ABE = ∆DBC SAS E D STATEMENTS REASONSP <none>S AB = BD GivenA 1=2 Vertical anglesS EB = BC Given∆’s ∆ABE = ∆DBC ˜ SAS
  15. 15. C Given: CX bisects ACB 12 A= B ˜ Prove: ∆ACX = ∆BCX ˜ AASA X BP CX bisects ACB GivenA 1= 2 Def of angle biscA A= B GivenS CX = CX Reflexive Prop∆’s ∆ACX = ∆BCX ˜ AAS
  16. 16. Can you prove these triangles are congruent?A B Given: AB ll DC X is the midpoint of AC X Prove: AXB = CXD ˜D C
  17. 17. A B Given: AB ll DC X is the midpoint of AC X Prove: AXB = CXD ˜D CASA
  18. 18. Triangle Congruence Triangle CongruenceSSS – If three sides of one triangle are congruent to three sides of SSS – If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent another triangle, then the two triangles are congruentSAS – If two sides and the included angle of one triangle are congruent SAS – If two sides and the included angle of one triangle are congruent to those of another triangle, then the two triangles are congruent to those of another triangle, then the two triangles are congruentASA – If two angles and the included side of one triangle are congruent ASA – If two angles and the included side of one triangle are congruent to those of another triangle, then the two triangles are congruent to those of another triangle, then the two triangles are congruentAAS – If two angles and a non-included side of one triangle are AAS – If two angles and a non-included side of one triangle are congruent to those of another triangle, then the two triangles are congruent to those of another triangle, then the two triangles are congruent congruentHL – If the hypotenuse and one leg of a right triangle are congruent to HL – If the hypotenuse and one leg of a right triangle are congruent to those of another right triangle, then the two triangles are those of another right triangle, then the two triangles are congruent congruent. .
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- SSS, SAS, AAS, ASA, HL - Unsing Triangle Congruence Properties

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