up of two rays that share the same endpoint.

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1 Space: Extends in all directions indefinitely Plane: A flat surface that extends indefinitely. Point: Has no length, no width, and no height, but it does have a location. Line: A set of points extending indefinitely in two directions. Segments Line, A piece of a line with two endpoints. A B Line segment AB or AB Rays Line, A part of a line with one endpoint. A B Ray AB or AB Angles Made named < ABC =< CBA or < x up of two rays that share the same endpoint. Rays BA and BC are sides of the angle Measure an angle :The unit of measurement is degree. Intersecting line: When two lines meet at a point, they are called intersecting lines. the lines CD and AB meet at point Transversal: A line that intersects two or more lines at different points.. If two parallel lines are cut by a transversal, then the measures of corresponding angles are equal and the measures of the alternate interior angles are equal.m n, find the measures of x, y, and z. Vertex (The common endpoint of an angle)b. Angles can be Classifying Angles Straight angle Right angle Acute \ə-ˈ kyüt\ angle measure is between 0 and 90. Obtuse angle measure is between 90 and 180. Two angles are said to be complementary the summation of their value gives 90 degrees If b = 110 then what would be the value of k? < x + < y = 90 When the values of two angles add up to 180 degrees they are called supplementary angles < 40 + < 140 = 180 Hw 8.1)1-55

2 Plane figure ˈ plān\ ˈ fi-gər\: A figure with length and width, but no thickness or depth, that lies on a plane. Polygon: \ˈ pä-lē-ˌ gän\ A closed plane figure that basically consists of three or more line segments that meet their end points Regular polygon : A closed plane figure whose sides are all the same length and whose angles are the same measure. Identifying Plane Figures Triangle \ˈ trī-ˌ aŋ-gəl\ Triangle Classification Equilateral : \ˌ ē-kwə-ˈ la-tə-rəl, ˌ e-, -ˈ la-trəl\ All three sides are the same length. Also, all three angles have the same measure Isosceles \ī-ˈ säs-ˌ lēz, -ˈ sä-sə-\ Two sides are the same length. Scalene : \ˈ skā-ˌ lēn, skā-ˈ \ A triangle having three sides of different lengths. The angles opposite the equal sides have equal measure. angles have the same measure. No The angles of an equilateral triangle all measure 60 degrees Quadrilateral \ˌ kwä-drə-ˈ la-t(ə- )rəl\ A four-sided polygon. Rectangle ˈ rek-ˌ taŋ-gəl\ A four-sided polygon having all right angles. Parallelogram \ˌ pa-rə-ˈ le-lə-ˌ gram\ A four-sided polygon with two pairs of parallel sides. The sum of the angles of a quadrilateral is 360 degrees. The sum of the angles of a rectangle is 360 degrees. The sum of the angles of a parallelogram is 360 degrees. Rhombus \ˈ räm-bəs\ A four-sided polygon having all four sides of equal length. Tapezoid \ˈ tra-pə-ˌ z id\ A four-sided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a rhombus is 360 degrees. Pentagon Hexagon \ˈ heksə-ˌ gän\ A six- \ˈ pen-tə-ˌ gän\ A five-sided sided The sum of the angles of a trapezoid is 360 degrees. Heptagon \ˈ hep-tə- ˌ gän\ A seven-sided Octagon \ˈ äk-tə- ˌ gän\ An eightsided polygon Nonagon ˈ nō-nə- ˌ gän\ A ninesided polygon Decagon \ˈ de-kə-ˌ gän\ A ten-sided polygon A regular pentagon polygon

3 Circle: circle is the collection of points in a plane that are all the same distance from a fixed point. The fixed point is called the center The blue line is the Radius\ˈ rā-dē-əs\ r, and the collection of red points is the circle. Diameter \dī-ˈ a-mə-tər\= Radius Identifying Solid Figures Solid\ˈ sä-ləd\a figure that lies in space and has length, width, and height or depth. Rectangular solid: A solid that consists of six sides, or faces, all of which are rectangles. Cube: A rectangular solid whose six sides are squares Pyramid: The pyramids we will study have square bases and heights that are perpendicular to their base. Sphere: \ˈ sfir\ Consists of all points in space that are the same distance from a point c, called the center of the sphere. Radius: The distance from the center to the sphere. Diameter: The distance across the sphere passing through the center. Cylinders: \ˈ silən-dər\ The cylinders we will study are in the shape of circles and have heights that are perpendicular to their base. Cones: \ˈ kōn\ The cones we will study have bases that are circles and heights that are perpendicular to their base.

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6 8.6 Square Roots and the square root of = 1 or because1 1 or 1 = is a perfect square because its square 1 root is a whole number or a fraction Approximate ap prox i mate the square root of 17 by using Appendix A.6 or a calculator because (4.13) 17 The square root of 17 must be approximated because it is not a perfect square Pythagorean \pə-ˌ tha-gə-ˈ rē-ən, (ˌ )pī-\ Theorem (leg) + (other leg) = (leg) + (other leg) = (hypotenuse) (hypotenuse) hypotenuse = (leg) + (other leg) leg = (hypotenuse) (other leg) Congruent and Similar Triangles