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GepubliceerdDavid Gerritsen Laatst gewijzigd meer dan 10 jaar geleden
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Just as an introduction for SDP-partners, this is a theoretical ppt on properties of triangles in which first, 3 properties are formulated and visualised (recalling or introducing new concepts) afterwards, 2 of these properties are proved while building up the proves interactively, pupils draw and write on prefab-sheets which combine multiple slides into 1 page (sheets are included here but not translated)
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7.3 Properties of triangles
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A C B A middle parallel of a triangle (a line connecting the middles of two sides of the triangle) is // with the third side and has half of its length 1)
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A C B Two medians of a triangle (lines through angle and middle of opposite side) divide each other in 2 parts which are in the ratio of 2 to 1 2) 2 1
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In a rectangular triangle the height onto the hypothenuse is middleproportional between the line segments 3) in which it divides the hypothenuse A C B h x y h 2 = x. y
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Een middenparallel van een driehoek (een lijnstuk dat de ……………………………………………………………… ………………………….. ) is // met de derde zijde en ……………………………. Gegeven: ABC met M het midden van [AB] en N het midden van [BC] Te bewijzen: MN // AC en …………………... Bewijs: Beschouw ABC en MBN : B = ………………….. = ……… (……………..) ABC …………………… M = A AB wordt door MN en AC gesneden volgens ……………………………….. ……………………………… …………………… |MN| = ……………… A C B
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A middle parallel of a triangle (a line which ………………………………………………………… is // with the third side ……………… Given: ABC with M the middle of [AB] and N the middle of [BC] To be proved: MN // AC and …………………... A C B connects the middles of two sides of the triangle) and has half of its length M N |MN| = |AC| 1)2)
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A C B M N Prove: Consider ABC and MBN : = ………………….. in common 2 (……….) ABC …………. MBN 1)
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A C B M N ABC …………. MBN 1) AB is cut by MN and AC according to ……………………………….. equal corresponding angles MN // AC
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A C B M N ABC …………. MBN 2) = 2 |MN| = |AC|
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In een rechthoekige driehoek is de hoogte op de schuine zijde ………….…………………………………. tussen de lijnstukken waarin ze de schuine zijde verdeelt. (zie p A.18) Gegeven: rechthoekige ABC met BH de hoogetlijn op [AC] Te bewijzen: |BH| 2 = |AH|.|HC| Bewijs: Beschouw AHB en BHC : A = …………………………………... C = …………………………………... (……….) AHB …………………… A C B ……………………….. of ………………………..
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In a rectangular triangle the heigth onto the hypothenuse is ………….………… between the line segments in which it divides the hypothenuse middleproportional A C B Given: rectangular ABC with BH the perpendicular onto [AC] To be proven: …………….. H |BH| 2 = |AH|.|HC|
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A C B H Prove: Consider AHB and BHC : Name the angles in B: 1 2 (angle angle) AHB BHC |BH| 2 = |AH|.|HC|
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… and now exercises …
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