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Congruent triangles
- 1.
- 2. When we talkabout 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. For us toprove that 2 people are identical twins, we don’t need to show that all “2000” body parts are equal. We can take a short cut and show 3 or 4 things are equal such as their face, age and height. If these are the same I think we can agree they are twins. The same is true for triangles. We don’t need to prove all 6 corresponding parts are congruent. We have 5 short cuts or methods.
- 4. SSS If we canshow all 3 pairs of corr. sides are congruent, the triangles have to be congruent.
- 5. SAS Show 2 pairsof sides and the included angles are congruent and the triangles have to be congruent. Included angle Non-included angles
- 6. This is calleda common side. It is a side for both triangles. We’ll use the reflexive property.
- 7. Which method canbe used to prove the triangles are congruent
- 8. Common side SSS Parallel lines altint angles Common side SAS Vertical angles SAS
- 10. ASA, AAS andHL A ASA – 2 angles and the included side AAS – 2 angles and The non-included side S A A A S
- 11. HL ( hypotenuseleg ) is used only with right triangles, BUT, not all right triangles. HL ASA
- 12. When Starting AProof, Make The Marks On The Diagram Indicating The Congruent Parts. Use The Given Info, Properties, Definitions, Etc. We’ll Call Any Given Info That Does Not Specifically State Congruency Or Equality A PREREQUISITE
- 13. SOME REASONS WE’LLBE 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
- 14. A C B 1 2 E SAS Given: AB= BD EB = BC Prove: ∆ABE = ∆DBC ˜ Our Outline P rerequisites D S ides A ngles S ides Triangles = ˜
- 15. A 1 E P S A S ∆’s C B 2 SAS D STATEMENTS none AB = BD 1=2 EB= BC ∆ABE = ∆DBC ˜ Given: AB = BD EB = BC Prove: ∆ABE = ∆DBC ˜ REASONS Given Vertical angles Given SAS
- 16. C 12 Given: CX bisectsACB A= B ˜ Prove: ∆ACX = ∆BCX ˜ AAS A X B P CX bisects ACB A 1= 2 A A= B S CX = CX ∆’s ∆ACX = ∆BCX ˜ Given Def of angle bisc Given Reflexive Prop AAS
- 17. Can you provethese triangles are congruent?
Editor's Notes
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