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- 1. CONGRUENT TRIANGLES Jim Smith JCHS Sections 4-3, 4-5
- 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 Vertical angles SAS SAS
- 9. PART 2
- 10. ASA, AAS and HL ASA – 2 angles and the included side A S A AAS – 2 angles and The non-included side 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 PROOFS
- 13. SOME REASONS WE’LL BE USING <ul><li>DEF OF MIDPOINT </li></ul><ul><li>DEF OF A BISECTOR </li></ul><ul><li>VERT ANGLES ARE CONGRUENT </li></ul><ul><li>DEF OF PERPENDICULAR BISECTOR </li></ul><ul><li>REFLEXIVE PROPERTY (COMMON SIDE) </li></ul><ul><li>PARALLEL LINES ….. ALT INT ANGLES </li></ul>
- 14. A B C D E 1 2 Given: AB = BD EB = BC Prove: ∆ABE ˜ ∆DBC = SAS Our Outline P rerequisites S ides A ngles S ides Triangles ˜ =
- 15. A C D Given: AB = BD EB = BC Prove: ∆ABE ˜ ∆DBC = B E 1 2 SAS none AB = BD Given 1 = 2 Vertical angles EB = BC Given ∆ ABE ˜ ∆DBC SAS = STATEMENTS REASONS P S A S ∆’ s
- 16. A B C 1 2 Given: CX bisects ACB A ˜ B Prove: ∆ACX ˜ ∆BCX X = = AAS P A A S ∆’ s CX bisects ACB Given 1 = 2 Def of angle bisc A = B Given CX = CX Reflexive Prop ∆ ACX ˜ ∆BCX AAS =
- 17. Can you prove these triangles are congruent? A B D C X Given: AB ll DC X is the midpoint of AC Prove: AXB ˜ CXD =
- 18. ASA A B D C X Given: AB ll DC X is the midpoint of AC Prove: AXB ˜ CXD =

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