Simultaneous Equations in the form A = B = C

Simultaneous Equations in the form A = B = C

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

Introduce Similar Triangles Edges, Vertices and Faces Edge Vertex (plural: vertices) Face Used more with 3D objects

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

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

SAS RHS

AAcorS

Notation & Definition Recall that if the two triangles below are congruent Y B We cant say ABC XZY A C

X Z We can say either ABC XYZ BAC YXZ CBA ZYX

ACB XZY BCA YZX CAB ZXY Example Explain why ABC and ADC are congruent. B A

C Note: The dots represent given angles that are the same size. D ABC ADC by SAS as BC = DC, AC AC (trivial, share the same line),

BCA = DCA Answers 1. ACB b. XYZ ACB by 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 EDC by 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) Similar Shapes What are similar shapes? Similar shapes are the same shapebut dont have to be the same size. These shapes are similar.

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. Answers Answers

Answers Answers Answers Answers Answers

Answers 4cm : Question 1x 2. 6cm x 3 5 2 :7.5c 2 5cm m : 5 These two 6cm

____ 4cm triangles are B A similar. Triangle A and B have heights 4cm and 6cm respectively. If triangle A has base 5cm,

what is the base of triangle B? 5cm ? Question 2 3cm 1cm 3cm 9cm

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

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