G9 - PPT ON CONGRUENCE - ASYNCHRONOUS - MAY 2024.ppt
- 2. When we talk about congruent triangles, When we talk about congruent triangles, we mean everything about them Is congruent. we mean everything about them Is congruent. All 3 pairs of corresponding angles are equal…. All 3 pairs of corresponding angles are equal…. And all 3 pairs of corresponding sides are equal And all 3 pairs of corresponding sides are equal
- 3. For us to prove that 2 people are For us to prove that 2 people are identical twins, we don’t need to show identical twins, we don’t need to show that all “2000” body parts are equal. We that all “2000” body parts are equal. We can take a short cut and show 3 or 4 can take a short cut and show 3 or 4 things are equal such as their face, age things are equal such as their face, age and height. If these are the same I think and height. If these are the same I think we can agree they are twins. The same we can agree they are twins. The same is true for triangles. We don’t need to is true for triangles. We don’t need to prove all 6 corresponding parts are prove all 6 corresponding parts are congruent. We have 5 short cuts or congruent. We have 5 short cuts or methods. methods.
- 4. SSS SSS If we can show all 3 pairs of corr. If we can show all 3 pairs of corr. sides are congruent, the triangles sides are congruent, the triangles have to be congruent. have to be congruent.
- 5. SAS SAS Show 2 pairs of sides and the Show 2 pairs of sides and the included angles are equal and included angles are equal and the triangles have to be congruent. the triangles have to be congruent. Included Included angle angle Non-included Non-included angles angles
- 6. This is called a common side. This is called a common side. It is a side for both triangles. It is a side for both triangles. We’ll use the reflexive property. We’ll use the reflexive property.
- 7. Which method can be used to Which method can be used to prove the triangles are congruent prove the triangles are congruent
- 8. Common side Common side SSS SSS Parallel lines Parallel lines alt int angles alt int angles Common side Common side SAS SAS Vertical angles Vertical angles SAS SAS
- 9. ASA, AAS and RHS ASA, AAS and RHS ASA – 2 angles ASA – 2 angles and the included side and the included side A A S S A A
- 10. When Starting A Proof, Make The When Starting A Proof, Make The Marks On The Diagram Indicating Marks On The Diagram Indicating The Congruent Parts. Use The Given The Congruent Parts. Use The Given Info, Properties, Definitions, Etc. Info, Properties, Definitions, Etc. We’ll Call Any Given Info That Does We’ll Call Any Given Info That Does Not Specifically State Congruency Not Specifically State Congruency Or Equality A Or Equality A PREREQUISITE PREREQUISITE
- 11. SOME REASONS WE’LL BE USING SOME REASONS WE’LL BE USING • DEF OF MIDPOINT DEF OF MIDPOINT • DEF OF A BISECTOR DEF OF A BISECTOR • VERT ANGLES ARE CONGRUENT VERT ANGLES ARE CONGRUENT • DEF OF PERPENDICULAR BISECTOR DEF OF PERPENDICULAR BISECTOR • REFLEXIVE PROPERTY (COMMON SIDE) REFLEXIVE PROPERTY (COMMON SIDE) • PARALLEL LINES ….. ALT INT ANGLES PARALLEL LINES ….. ALT INT ANGLES
- 12. A A B B C C D D E E 1 1 2 2 Given: AB = BD Given: AB = BD EB = BC EB = BC Prove: Prove: ∆ABE ∆ABE ˜ ˜ ∆DBC ∆DBC = = SAS SAS Our Outline Our Outline P P rerequisites rerequisites S S ides ides A A ngles ngles S S ides ides Triangles ˜ Triangles ˜ = =
- 13. A A C C D D Given: AB = BD Given: AB = BD EB = BC EB = BC Prove: Prove: ∆ABE ∆ABE ˜ ˜ ∆DBC ∆DBC = = B B E E 1 1 2 2 SAS SAS = = STATEMENTS REASONS STATEMENTS REASONS P P S S A A S S ∆’ ∆’s s
- 14. Can you prove these triangles Can you prove these triangles are congruent? are congruent?