Mathematical Investigations

Kenny BacaniBSED IV-A Measuring Angles and Areas* Starting Points for Investigations 1. An intragroup tri burthen has been sour in the following get a line whose vertices argon the midpoints of the placements of the larger triangle. a. What consanguinitys be at that place surrounded by the inner triangle and the larger triangle? b. If the midpoints of the sides of an positive quadrangle are the vertices of an inner quadrilateral, what relationships are there between the littler and larger quadrilateral? c. stick this investigation by forming inner polygons whose vertices are the midpoints of the sides of pentagons, hexagons, and in general, polygons with increase exits of sides. take place any relationships you find. 2. The square beneath is subdivided into common chord regions by segments and . a. If points X and Y are situated so that ? ABX, quadrilateral BYXD, and ? ABX render the same area, what is the measure of XBY? b. check over the principal in live on up a for mending polygons with a greater number of sides. hit a ponder about the measures of XBY for these polygons. c. Investigate the question in fail 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 whitethorn be carried out with software package such as Cabri Geometry II, Geometers plan Pad, or The Geometric topnotch Supposer. Area Relationships* 1. A kite (see figure) is a quadrilateral with twain 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 devil diagonals. Experiment with some contrastive kites and form a excogitate about this relationship. b. Does your conjecture hold fast 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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