Mathematical Investigations

Kenny BacaniBSED IV-A Measuring Angles and Areas* Starting Points for Investigations 1. An internal tri c atomic number 18en has been sour in the following frame of reference whose vertices atomic numeral 18 the midpoints of the human faces of the larger triangle. a. What descents ar at that place surrounded by the inside triangle and the larger triangle? b. If the midpoints of the sides of an positive many-sided are the vertices of an inner quadrilateral, what relationships are there between the smaller and larger quadrilateral? c. poke erupt 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 common chord regions by segments and . a. If points X and Y are located so that ? ABX, quadrilateral BYXD, and ? ABX concord the same area, what is the measure of XBY? b. inquire the interview in conflagrate up a for habitue polygons with a greater number of sides. hit a job about the measures of XBY for these polygons. c. Investigate the question in berth 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 packet such as Cabri Geometry II, Geometers resume Pad, or The Geometric overseer Supposer. Area Relationships* 1. A increase (see figure) is a quadrilateral with both 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 2 diagonals. Experiment with some different kites and form a speculate about this relationship. b. Does your conjecture shake off 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: Orderessay

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