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Congruent triangles – Part 2

Congruent triangles – Part 2. Slideshow 39, Mathematics Mr Richard Sasaki, Room 307. Objectives. Understand and recall some shape properties (in particular the right-angled triangle) Practice showing whether triangles are congruent or not using rules given last lesson

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Congruent triangles – Part 2

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  1. Congruent triangles– Part 2 Slideshow 39, Mathematics Mr Richard Sasaki, Room 307

  2. Objectives Understand and recall some shape properties (in particular the right-angled triangle) Practice showing whether triangles are congruent or not using rules given last lesson Introduce Similar Triangles

  3. Edges, Vertices and Faces Edge Vertex (plural: vertices) Face – Used more with 3D objects

  4. Right-Angled Triangle Hypotenuse Opposite Adjacent Each edge has a special name for a right-angled triangle in respect to another angle.

  5. Triangle Congruency Testing Rules We have learned 4 laws to test congruency. Which is which? SSS SAS RHS AAcorS

  6. Notation & Definition Recall that if the two triangles below are congruent… Y B We can’t say ∆ABC ≅ ∆XZY A C X Z We can say either… ∆ACB ≅ ∆XZY ∆ABC ≅ ∆XYZ ∆BCA ≅ ∆YZX ∆BAC ≅ ∆YXZ ∆CAB ≅ ∆ZXY ∆CBA ≅ ∆ZYX

  7. Example Explain why ∆ABC and ∆ADC are congruent. B Note: The dots “●” represent given angles that are the same size. C A D ∆ABC ≅∆ADCby SAS as… BC = DC, AC AC (trivial, share the same line), BCA = DCA

  8. Answers ACB b. ∆XYZ ≅ ∆ACBby SAS as…XY = AC, YZ = CB and XYZ = ACB 2. We are given the information for AAcorS. The edge given between both 70o angles are different sizes (5m and 5cm) 3. ∆ABC ≅ ∆EDCby SAS as… AC = CE, BC = CD and ACB = DCE (opposite angles) b. 37o as they are alternate angles (the same angle on both congruent triangles)

  9. Similar Shapes What are similar shapes? Similar shapes are the same shape…but don’t have to be the same size. These shapes are similar.

  10. Similar Shapes To be the same “shape”, the shapes must be in the same proportion. These shapes are not similar. Note: Congruent shapes are also similar shapes. If the size is also the same, they are still similar.

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  19. 4cm : 6cm 2 : 3 5cm : ____ Question 1 x 2.5 x 2.5 7.5cm These two triangles are similar. 6cm B A 4cm 5cm ? Triangle A and B have heights 4cm and 6cm respectively. If triangle A has base 5cm, what is the base of triangle B?

  20. Question 2 3cm 3cm 3cm 9cm 10cm 1cm 1. Split the rectangle into 2 similar rectangles that are not congruent. 2. Prove that the flashing length is 3cm using the method in Question 1.

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