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1-1 Understanding Points, Lines, and Planes Vocabulary undefined term line collinear segment ray postulate Holt Geometry point plane coplanar endpoint opposite rays 1-1 Understanding Points, Lines, and Planes Holt Geometry 1-1 Understanding Points, Lines, and Planes Holt Geometry 1-1 Understanding Points, Lines, and Planes Holt Geometry 1-1 Understanding Points, Lines, and Planes Holt Geometry 1-2 Measuring and Constructing Segments Vocabulary coordinate midpoint distance bisect length segment bisector construction between congruent segments Holt Geometry 1-2 Measuring and Constructing Segments In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC. Holt Geometry 1-2 Measuring and Constructing Segments The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. Holt Geometry 1-3 Measuring and Constructing Angles Vocabulary angle vertex interior of an angle exterior of an angle measure degree acute angle Holt Geometry right angle obtuse angle straight angle congruent angles angle bisector 1-3 Measuring and Constructing Angles The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is of a circle. When you use a protractor to measure angles, you are applying the following postulate. Holt Geometry 4 Types of Angles Acute Angle: an angle whose measure is less than 90. Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between 90 and 180. Straight Angle: an angle that is exactly 180 . Lesson 1-4: Angles 11 1-3 Measuring and Constructing Angles Holt Geometry 1-3 Measuring and Constructing Angles An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Holt Geometry 1-4 Pairs of Angles Vocabulary adjacent angles linear pair complementary angles supplementary angles vertical angles Holt Geometry 1-4 Pairs of Angles Holt Geometry 1-4 Pairs of Angles Holt Geometry 1-4 Pairs of Angles Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical angles are two nonadjacent angles formed by two intersecting lines. 1 and 3 are vertical angles, as are 2 and 4. Holt Geometry 1-5 Using Formulas in Geometry Vocabulary perimeter area base height Holt Geometry diameter radius circumference pi 1-5 Using Formulas in Geometry The perimeter P of a plane figure is the sum of the side lengths of the figure. The area A of a plane figure is the number of non-overlapping square units of a given size that exactly cover the figure. Holt Geometry 1-5 Using Formulas in Geometry Holt Geometry 1-5 Using Formulas in Geometry The ratio of a circle’s circumference to its diameter is the same for all circles. This ratio is represented by the Greek letter (pi). The value of is irrational. Pi is often approximated as 3.14 or . Holt Geometry 1-6 Midpoint and Distance in the Coordinate Plane Vocabulary coordinate plane leg hypotenuse Holt Geometry The x-axis and y-axis separate the coordinate plane into four regions, called quadrants. II (-, +) III (-, -) I (+, +) IV (+, -) 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry 1-6 Midpoint and Distance in the Coordinate Plane The Ruler Postulate can be used to find the distance between two points on a number line. The Distance Formula is used to calculate the distance between two points in a coordinate plane. Holt Geometry 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry 1-7 Transformations in the Coordinate Plane Vocabulary transformation preimage image Holt Geometry reflection rotation translation 1-7 Transformations in the Coordinate Plane The Alhambra, a 13th-century palace in Grenada, Spain, is famous for the geometric patterns that cover its walls and floors. To create a variety of designs, the builders based the patterns on several different transformations. A transformation is a change in the position, size, or shape of a figure. The original figure is called the preimage. The resulting figure is called the image. A transformation maps the preimage to the image. Arrow notation () is used to describe a transformation, and primes (’) are used to label the image. Holt Geometry 1-7 Transformations in the Coordinate Plane Holt Geometry 1-7 Transformations in the Coordinate Plane To find coordinates for the image of a figure in a translation, add a to the x-coordinates of the preimage and add b to the y-coordinates of the preimage. Translations can also be described by a rule such as (x, y) (x + a, y + b). Holt Geometry