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Congruent triangles – Part 1

Congruent triangles – Part 1. Slideshow 38, Mathematics Mr Richard Sasaki, Room 307. Starter. Please answer the questions on the worksheet provided. You will need protractors, you may use your own or borrow one. Starter - Answers. Starter - Answers. Starter - Answers. Starter - Answers.

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Congruent triangles – Part 1

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  1. Congruent triangles– Part 1 Slideshow 38, Mathematics Mr Richard Sasaki, Room 307

  2. Starter Please answer the questions on the worksheet provided. You will need protractors, you may use your own or borrow one.

  3. Starter - Answers

  4. Starter - Answers

  5. Starter - Answers

  6. Starter - Answers

  7. Starter - Answers

  8. Starter - Answers

  9. Objectives • Understand the ways and names of ways that we can test if two triangles are congruent • Use these rules to state whether triangles are congruent and find missing angles

  10. Congruent Triangles When two Triangles are the same size and shape, they are congruent. If we have information that produces a unique triangle, we can check to see if it is congruent to another. Check the two worksheets from the last two lessons.

  11. Drawing unique triangles The minimum amount of information needed is either: • Three edges • One edge and two angles • Two edges and one angle (In special cases)

  12. Congruent Triangles With this information we can check whether two triangles are congruent: 5cm 4cm 5cm 4cm 4cm 4cm 60o 80o 60o 80o 2cm 2cm (AAcorS) (SSS) One edge and two angles Three edges

  13. AAcorS? This means “Two angles and a corresponding side”. 4cm 4cm 60o 80o 60o 80o (AAcorS) The angles must be in the same place in relation to the side. One edge and two angles Note: These are not congruent… 60o 4cm 4cm 80o 60o 80o

  14. Congruent Triangles With this information we can check whether two triangles are congruent: 40o 40o 5cm 4cm 5cm 4cm 5cm 5cm 3cm 3cm (RHS) (SAS) Two edges with an angle between them The hypotenuse and any other corresponding side

  15. Note: Hypotenuse is the longest edge. RHS? RHS Means “Right Hypotenuse side” but really this rule works for any two sides on a right-angled triangle. 5cm 5cm 3cm 3cm (RHS) The hypotenuse and any other side Note: These are Also congruent by SAS. 4cm 4cm 3cm 3cm

  16. Answers b. SSS 2. yes, no, yes, no, yes 3. ∆ABC ≅ ∆YXZby SAS as AB=YX, BC=XZ and ABC = YXZ. 4. ∆ABC ≅ ∆XZYby RHS as AB = XZ, BC = YZ and ACB = XYZ which are both right-angles b. 5. The two angles and edge are the same size but don’t correspond.

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