ACING THE GED EXAM phần 9

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ACING THE GED EXAM phần 9 – THE GRE QUANTITATIVE SECTION – The area of a sector is found in a similar way to finding the length of an arc. To find the area of a sector, sim- xply multiply the area of a circle, πr2, by the fraction 360 , again using x as the degree measure of the central angle. Example: Given x = 60º and r = 8, find the area of the sector: r o x r 60 ( )82 A= 360 1 A= 64( ) 6 64 A= 6( ) 32 A= 2( )Polygons and ParallelogramsA polygon is a closed figure with three or more sides. B C A D F E T ERMS R ELATED P OLYGONS TO Vertices are corner points, also called endpoints, of a polygon. The vertices in the previous polygon are ■ A, B, C, D, E, and F. A diagonal of a polygon is a line segment between two nonadjacent vertices. The two diagonals indi- ■ cated in the previous polygon are line segments BF and AE. A regular (or equilateral) polygon’s sides are all equal. ■ An equiangular polygon’s angles are all equal. ■ 191 – THE GRE QUANTITATIVE SECTION – A NGLES Q UADRILATERAL OF AA quadrilateral is a four-sided polygon. Since a quadrilateral can be divided by a diagonal into two trian-gles, the sum of its angles will equal 180 + 180 = 360 degrees. 2 1 3 4 m∠1 + m∠2 + m∠3 + m∠4 = 360° I NTERIOR A NGLESTo find the sum of the interior angles of any polygon, use this formula: S = 180(x – 2)where x is the number of polygon sides. Example: Find the sum of the angles in the following polygon. 2 3 1 4 5 S = (5 – 2) 180 S = 3 180 S = 540 E XTERIOR A NGLESSimilar to the exterior angles of a triangle, the sum of the exterior angles of any polygon equals 360 degrees. 192 – THE GRE QUANTITATIVE SECTION – S IMILAR P OLYGONSIf two polygons are similar, their corresponding angles are equal and the ratio of the corresponding sides isin proportion. Example: 4 2 120° 10 120° 5 6 3 60° 60° 18 9 These two polygons are similar because their angles are equal and the ratio of the corresponding sidesis in proportion.ParallelogramsA parallelogram is a quadrilateral with two pairs of parallel sides. B C A DIn this figure, AB CD and BC AD.A parallelogram has the following characteristics: Opposite sides are equal (AB = CD and BC = AD). ■ Opposite angles are equal (m A = m C and m B = m D). ■ Consecutive angles are supplementary (m A + m B = 180º, m B + m C = 180º, ■ m C + m D = 180º, m D + m A = 180º). Diagonals bisect each other. ■ S PECIAL T YPES PARALLELOGRAMS OFThere are three types of special parallelograms: A rectangle is a parallelogram that has four right angles. ■ ...