Consider a polygon of n sides For the concave quadrilateral ABCD,

In Chapter 4, we will discover formal definitions of the types of quadrilaterals known as the parallelogram, square, rectangle, kite, rhombus, and rectangle. Some of these are included in Examples 3 and 5. EXAMPLE 1 Rectangle ABCD in Figure 2.38 on page 107 has a second line of symmetry. Draw this line or axis for which there is vertical symmetry. Solution Line m determined by the midpoints of and is the desired line of symmetry. As shown in Figure 2.39b, R and S are located symmetrically with respect to line m. 쮿 BC AD Geometry in Nature Like many of nature’s creations, the butterfly displays line symmetry. © Photo Researchers,Inc. EXAMPLE 2 a Which letters shown below has have a line of symmetry? b Which letters has have more than one line of symmetry? B D F G H Solution a B, D, and H as shown b H as shown Discover The uppercase block form of the letter A is shown below. Does it have symmetry with respect to a line? ANSWER Yes, line 艎 as shown is a line of symmetry. This vertical line 艎 is the only line of symmetry for the uppercase A. A D C B m Figure 2.39 A D C B m R S 쮿 a b EXAMPLE 3 a Which figures have at least one line of symmetry? b Which figures have more than one line of symmetry? POINT SYMMETRY In Figure 2.41, rectangle ABCD is also said to have symmetry with respect to a point. As shown, point P is determined by the intersection of the diagonals of rectangle ABCD. Exs. 1–4 Solution a The isosceles triangle, square, and the regular pentagon all have a line of symmetry. b The square and regular pentagon have more than one line of symmetry, so these figures are shown with two lines of symmetry. There are actually more than two lines of symmetry. 쮿 Figure 2.40a Isosceles Triangle Square Quadrilateral Regular Pentagon Isosceles Triangle Figure 2.40b Square Regular Pentagon Figure 2.41 A figure has symmetry with respect to point P if for every point M on the figure, there is a second point N on the figure for which point P is the midpoint of MN. DEFINITION a b