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Published byDarcy Jackson Modified over 9 years ago
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Outcome: SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
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Labelling and naming triangles and quadrilaterals in text and on diagrams The triangle is named Δ ABC The angle at A could be named BAC, CAB, A, BÂC or a ̊ The quadrilateral is named ABCD A B C A B D C
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Using the common conventions to mark equal intervals on diagrams
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Recognising and classifying types of triangles on the basis of their properties Triangles classified by interior angles Acute Right Obtuse (All angles acute) ( 1 right angle) (1 obtuse angle) (0-90 ̊) ( 90 ̊) (90-180 ̊)
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Triangles classified by side lengths ScaleneIsoscelesEquilateral (no side equal) ( 2 sides equal) ( 3 sides equal) Base angles equal l ll lll l l l l l x ●○ ●● 60 ̊
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Justifying informally that the interior angle sum of a triangle is 180 ̊.
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The exterior angle equals the sum of the two interior angles opposite angles. = + 2 opposite interior s exterior
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Using a parallel line construction, to prove that the interior angle sum of a triangle is 180 ̊. As these two lines are parallel, we can use the alternate (or z angle) fact to label the two exterior angles and as below. We know that the angle on a straight line on a straight line is 180°, so we can say that + + = 180°. Therefore the interior angles of a triangle add up to 180°.
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Using a parallel line construction, that any exterior angle sum of a triangle is equal to the sum of the two interior opposite angles. + + exterior s
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Establishing that the angle sum of a quadrilateral is 360 ̊. 180 ̊
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Let’s start developing the rule ShapeNumber of sides Number of triangles Angle sum triangle311 x 180 ̊ = 180 ̊ quadrilateral422 x 180 ̊ = 360 ̊ pentagon53 _ x 180 ̊ = __ hexagon6_ x 180 ̊ = __ heptagon7_ x 180 ̊ = __ octagon8_ x 180 ̊ = __ n-sided polygon n( __ ) x 180 ̊=
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