Mathematical Investigations

Kenny BacaniBSED IV-A Measuring Angles and Areas* Starting Points for Investigations 1. An inner triangle has been sour in the following public figure whose vertices atomic number 18 the midpoints of the sides of the bigger triangle. a. What human relationships atomic number 18 at that place surrounded by the inner triangle and the larger triangle? b. If the midpoints of the sides of an positive quadrilateral are the vertices of an inner quadrilateral, what relationships are there between the smaller and larger quadrilateral? c. brood this investigation by forming inner polygons whose vertices are the midpoints of the sides of pentagons, hexagons, and in general, polygons with change magnitude numbers of sides. take out any relationships you find. 2. The square at a lower place is subdivided into three regions by segments and . a. If points X and Y are placed so that ? ABX, quadrilateral BYXD, and ? ABX grant the same area, what is the measure of XBY? b. go over the question in break up a for symmetrical polygons with a greater number of sides. hit a opine about the measures of XBY for these polygons. c. Investigate the question in bring out a for a circle. That is, what is the measure of XBY, if the areas of the three regions formed by segments and are equal? How does the measure of this angle comparison to the measures of the angles in part b? *This investigation may be carried out with software package such as Cabri Geometry II, Geometers Sketch Pad, or The Geometric exceedingly Supposer. Area Relationships* 1. A kite (see figure) is a quadrilateral with 2 non overlapping pairs of adjacent sides that are congruent. a. thither is an interesting relationship between the area of a kite and the product of its ii diagonals. Experiment with some different kites and form a anticipate about this relationship. b. Does your conjecture hold for new(prenominal) quadrilaterals such as squares, rectangles, parallelogra ms, and trapezoids? 2. A square has been co! nstructed on each(prenominal) side of triangle T (see figure below). The shaded triangles...If you want to give a full essay, order it on our website: BestEssayCheap.com

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