Mathematical Investigations

Kenny BacaniBSED IV-A Measuring Angles and Areas* Starting Points for Investigations 1. An inner triangle has been sour in the following move into whose vertices argon the midpoints of the sides of the large triangle. a. What consanguinitys 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. touch 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 on a lower floor is subdivided into three regions by segments and . a. If points X and Y are locate so that ? ABX, quadrilateral BYXD, and ? ABX grant the same area, what is the measure of XBY? b. study the question in break up a for standard polygons with a greater number of sides. hit a scheme about the measures of XBY for these polygons. c. Investigate the question in image 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 bundle such as Cabri Geometry II, Geometers Sketch Pad, or The Geometric super Supposer. Area Relationships* 1. A kite (see figure) is a quadrilateral with dickens non overlapping pairs of adjacent sides that are congruent. a. thither is an int! eresting relationship between the area of a kite and the product of its 2 diagonals. Experiment with some different kites and form a reckon about this relationship. b. Does your conjecture hold for new(prenominal) quadrilaterals such as squares, rectangles, parallelograms, and trapezoids? 2. A square has been constructed 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: OrderCustomPaper.com

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