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Download The sum of its interior angles is 180(n – 2). The sum of the exterior
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Transcript
Ch 5 Summary with Tree Diagram Key Name ____________________________ Chapter 5: Discovering and Proving Polygon Properties Properties of Polygons Properties of Equiangular Polygons The sum of its interior angles is 180(n – 2). The sum of the exterior angles is 360. n ( n − 3) diagonals. Polygon of n sides has 2 The measure of each interior angle is ( n − 2)180 360 or 180 − n n The measure of each exterior angle is 360/n. Midsegment (of a triangle) is the line segment connecting the midpoints of two sides of the triangle. The three midsegments of a triangle divide it into four congruent triangles. A midsegment of a triangle is: parallel to the third side and half the length of the third side. Midsegment (of a trapezoid) is the line segment connecting the midpoints of the two nonparallel sides. The midsegment of a trapezoid is: parallel to the bases and equal in length to the average of the lengths of the bases. m= a+b 2 a m b Ch 5 Summary with Tree Diagram Key Name ____________________________ Quadrilateral Def.: A four-sided polygon. Sum of the interior angles is 360. Kite Def.: A quad. with exactly two distinct pairs of consecutive congruent sides. The nonvertex angles are congruent. The diagonals are perpendicular. The diagonal between the vertex angles bisects the other diagonal. It has exactly one line of symmetry. Parallelogram Def.: A quad with [both pairs] opposite sides parallel. Trapezoid Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. Consecutive angles between the bases are supplementary. Rhombus Rectangle Def.: An equilateral parallelogram [4 sides congruent]. Def.: An equiangular parallelogram. Diagonals are perpendicular bisectors of each other. Diagonals bisect the opposite pairs of angles. Each angle measures 90 [all right angles]. Diagonals are congruent. Def.: A quad with exactly one pair of parallel sides. Isosceles Trapezoid Def.: A trapezoid whose legs are the same length. Base angles are congruent. Diagonals are congruent. Square Def.: An equiangular rhombus or an equilateral rectangle. Diagonals form many 45:45:90 triangles.