Congruent Triangles

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Introduces the 5 conditions for congruent triangles

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Congruent Triangles

  1. 1. Triangle Style
  2. 2. WHAT IS CONGRUENCY? When two shapes are exactly the same size and shape we say they are CONGRUENT WHICH OF THESE SHAPES IS CONGRUENT WITH THE FIRST SHAPE?
  3. 3. Too small Too big Even though their direction changed, they are the same size and shape.
  4. 4. WHICH OF THE FOLLOWING ARE CONGRUENT?
  5. 5. WHICH OF THE FOLLOWING ARE CONGRUENT?
  6. 6. THERE ARE 5 CONDITIONS WE CAN USE TO DETERMINE IF 2 TRIANGLES ARE CONGRUENT • • • • • SSS -- Side-Side-Side SAS – Side-Angle-Side ASA – Angle-Side-Angle AAS – Angle-Angle-Side RHS – Right-Hypotenuse-Side
  7. 7. WHY DO THEY WORK? These rules work because they show us the MINIMUM information we need to know to be able to use Geometry to determine the remaining angles and side lengths. Therefore, if we memorize these rules, we can know immediately if triangles are congruent or not.
  8. 8. SIDE – SIDE – SIDE Just like for the images, if all the sides of a triangle are the same, then that must mean that the triangles are congruent. This is known as the Side-Side-Side condition or SSS
  9. 9. SIDE – ANGLE – SIDE If you know two sides and a single angle, we can determine the final leg length and angles, therefore we know these angles must be congruent. This is known as the Side-Angle-Side condition or SAS
  10. 10. ANGLE – SIDE – ANGLE If we know two angles and a side we can use geometry to determine the other angles and sides, therefore we can determine that the triangles have the same angles and side lengths. Therefore we only need to know 2 angles and 1 side to determine that the triangles are congruent. This is known as the Angle-Side-Angle condition or ASA
  11. 11. ANGLE – ANGLE – SIDE If we know two angles and a side we can use geometry to determine the other angles and sides, therefore we can determine that the triangles have the same angles and side lengths. Therefore we only need to know 2 angles and 1 side to determine that the triangles are congruent. This is known as the Angle-Angle-Side condition or AAS
  12. 12. RIGHT – HYPOTENUSE – SIDE If we know one angle is a right angle, and we know the hypotenuse and a side, we can determine the rest of the angles and sides using geometry. Therefore we only need to know that there is a right angle and the lengths of the hypotenuse and one side to determine the triangles are congruent. This is known as the Right Hypotenuse Side condition RHS
  13. 13. RULES THAT DON’T WORK
  14. 14. ANGLE – ANGLE – ANGLE If all angles are the same that does not mean they are congruent. The leg lengths could be different.
  15. 15. SIDE – SIDE – ANGLE Even if we know two sides and an angle, we do not have enough information to determine the rest of the triangle’s features.
  16. 16. PRACTICE – ARE THESE CONGRUENT? IF SO BY WHICH CONDITION?
  17. 17. PRACTICE – ARE THESE CONGRUENT? IF SO BY WHICH CONDITION? YES-ASA
  18. 18. NO- AAA IS NOT A CONDITION FOR CONGRUENCY.
  19. 19. NO –SSA IS NOT A CONDITION FOR CONGRUENCY
  20. 20. YESSSS
  21. 21. YES - SAS
  22. 22. YESAAS
  23. 23. YES – RHS

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