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| === Objectives === | | === Objectives === |
− | # Understand properties of triangles – a segment connecting mid-points of two sides of a triangle will be parallel to the third side and its length will be half of the third side | + | # To guide and facilitate student exploration of the properties of triangles, specifically – a segment connecting mid-points of two sides of a triangle will be parallel to the third side and its length will be half of the third side. |
− | # Demonstrate that the line joining the mid-points of any two sides of a triangle is parallel to the third side and equals to half the third side | + | # To introduce theorems associated with triangles |
| + | # To demonstrate the steps of logical proof and the processes |
| + | # Understand properties of triangles |
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| === Estimated Time === | | === Estimated Time === |
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| === Prerequisites/Instructions, prior preparations, if any === | | === Prerequisites/Instructions, prior preparations, if any === |
− | Prior knowledge of point, lines, angles, parallel lines, triangles, and quadrilaterals / parallelograms
| + | An understanding of the basic elements of geometry. Students are familiar with angles and parallel lines, and have been introduced to the concepts of parallelogram |
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| === Materials/ Resources needed === | | === Materials/ Resources needed === |
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| Work sheet | | Work sheet |
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− | Each group member will construct on her / his notebook, using pencil, scale, protractor, and compass a triangle, with the measures provided | + | Each group member will construct on her / his notebook, using pencil, scale, protractor, and compass a triangle, with the measures provided. You can make chits that have triangle measures. You can even repeat them. For a group give the following. One acute. One obtuse. One equilateral. One isosceles. One right. Provide only measures, for e.g. |
| + | # Draw a triangle with following measures - BC = 6 cms, AC = 7 cms, AB = 8 cms (BC as the base) |
| + | # Draw a triangle with following measures BC = 8 cms, angle B = 110, AB = 6 cms (BC as the base) |
| + | # Draw a triangle with following measures BC = 10 cms, angle B = 60, angle C = 60 (BC as the base) |
| + | # Draw a triangle with following measures BC = 12 cms, angle B = 90, AC = 13 cms (BC as the base) |
| + | # Draw a triangle with following measures BC = 8 cms, angle B = 40, angle C = 40 (BC as the base) |
| + | # Draw a triangle with following measures BC = 6 cms, angle B = 110, AB = 5 cms (BC as the base) |
| + | # Draw a triangle with following measures BC = 8 cms, angle B = 60, angle C = 40 (BC as the base) |
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− | # Students should plot the mid-point of two sides and connect these with a line segment. Show [[:File:Mid-point theorem 1.ggb|Mid-point theorem1.ggb]] step by step. | + | Each group gets this set and each member picks one chit and makes a sketch |
| + | # Students should plot the mid-point of two sides (Segment AB, and AC, as D and E) and connect these with a line segment (Join these mid-points D and E. Label it Segment DE). Show [[:File:Mid-point theorem 1.ggb|Mid-point theorem1.ggb]] step by step. |
| ## They should measure the length of this segment and length of the third side and check if there is any relationship | | ## They should measure the length of this segment and length of the third side and check if there is any relationship |
| ## They should measure the angles formed at the two vertices connecting the third side, with the two angles formed on the two mid-points | | ## They should measure the angles formed at the two vertices connecting the third side, with the two angles formed on the two mid-points |