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Congruent triangles
- 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. For us to prove 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 can show all 3 pairs of corr. sides are congruent, the triangles have to be congruent.
- 5. SAS Show 2 pairs of sides and the included angles are congruent and the triangles have to be congruent. Included angle Non-included angles
- 6. This is called a common side. It is a side for both triangles. We’ll use the reflexive property.
- 7. Which method can be used to prove the triangles are congruent
- 8. Common side SSS Parallel lines alt int angles Common side SAS Vertical angles SAS
- 10. ASA, AAS and HL A ASA – 2 angles and the included side AAS – 2 angles and The non-included side S A A A S
- 11. HL ( hypotenuse leg ) is used only with right triangles, BUT, not all right triangles. HL ASA
- 12. When Starting A Proof, 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’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
- 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 bisects ACB 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 prove these triangles are congruent?
Editor's Notes
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