Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26)

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1 Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26) Learning Target: At the end of today s lesson we will be able to successfully name and sketch geometric figures. In Geometry there are 3 UNDEFINED TERMS. 1.) 2.) 3.) These words DO NOT have formal definitions, but there is agreement about what they mean. Vocabulary Description Illustration Point Line Plane Example 1: 1. A point has dimension. 2. It is represented by a. 1. Line A line has dimension. 2.It is represented by a with two arrowheads. 3. It extends in two directions. 4. Through any points, there is exactly line. 5. You can use any points on a line to name it or case cursive letter. 1. Has dimensions. 2. It is represented by a shape that looks like a floor or wall, but it extends without end. 3. Through any points not on the same line, there is exactly plane. 4. You can use three points that are all on the same line to name a plane. Name : Name: Name: a. Give two other name for LN, b. Give another name for plane Z. c. Name three points that are collinear (Points on the same line.).,, d. Name four points that are coplanar. (Points on the same, but not on the same line).,,, Example 2: Use the diagram in Example 1. a. Give two other names for MQ b. Name a point that is not coplanar with points L, N, and P. Defined Terms: In Geometry, these are terms that can be described using words such as point or line.

2 Line: Line AB (written as ) and points A and B are used here to define the terms below: Segment: The line segment AB, or segment AB, (written as ) consists of the endpoints A and B and all points on that are A and B. Ray: The ray AB (written as ) consists of the endpoints A and all points on that lie on the same side of as. Note: and are two rays! Opposite Rays: If point C lines on line AB between A and B, then and are opposite rays. Illustration: Note: Opposite rays form a angle! Example 3: a. Give another name for. b. Name all rays with endpoints W. c. Which of these rays are opposite rays? & d. WX and WY have a common, but are not. So they are not opposite rays. e. Give another name for. f. Are and the same ray? Are and the same ray? Intersecting Figures: The intersection of two or more geometric figures is the set of points that the figures have in. Description Sketch Intersection Two crossing lines Intersection of two different planes A plane and a line that intersect in one spot A plane and a line that is in the plane

3 Geometry Lesson 1-2 Goal: Use Segments and Congruence Name HR Pg 11 ( 1,6-12, 16-19, 21-30, 37, 38) Show ALL work for credit!!! Learning Target: At the end of today s lesson we will be able to successfully use segment postulates to identify congruent segments. Postulate/Axiom: In Geometry, a rule that is without proof. Theorem: A rule that can be. Postulate 1: The Ruler Postulate The points on a line can be matched one to one with real numbers. The real number that corresponds to a point is the coordinate of the point. Absolute value: The distance between points A and B, written as, is the absolute value of the of the coordinates of A and B. AB is also called the of AB. (Note: Absolute values are ALWAYS.) Example 1: a.) Measure the length of AB to the nearest tenth of a centimeter. b.) Use the number line to find each length below. DE BD AE AC

4 Three Collinear Points: When three points are collinear, you can say that one point is the other two on the same line. Postulate 2: The Segment Addition Postulate If B is between A and C, then If AB + BC = AC, then B is between and Example 2: Example 3: Example 4: Congruent Line Segments: Line segments that have the length. Example 5:

5 Name Hr Geometry Lesson 1-3 Goal: Use Distance and Midpoint Formulas Pg 19 (1,2-24 even, even) Show ALL work for credit!!! Learning Target: At the end of today s lesson we will be able to successfully find lengths of segments in the coordinate plane. Midpoint: The point that divides the segment into two CONGRUENT segments. If M is the midpoint of the segment above, then & = Segment Bisector: A point, line, line segment, or plane that intersects the segment at its. & = & = & = & = Example 1: a.) b.)

6 Example 2: a.) Point M is the midpoint of GH. b.) Point M is the midpoint of PQ. Midpoint Formula The coordinates of the midpoint of a segment are the of the x-coordinates and of the y- coordinates of the endpoints. If A(x 1,y 1 )and B(x 2, y 2 ) are points in a coordinate plane, then the midpoint M of AB has coordinates: (M x, M y ) = Example 5: Find Midpoint: The endpoints of PR are P( 2, 5) and R(4, 3). Find the coordinates of the midpoint M. The Distance Formula: If A(x 1, y 1 ) and B(x 2, y 2 ) are points in a coordinate plane, then the distance between A and B is: AB = + Example 6: What is the approximate length of segment RT, with endpoints R(3, 2) and T( 4, 3)?

The rays are the of the angle. The endpoint is the of the angle. The angle at the left has sides and The angle can be named,, or. is the vertex of the angle.

7 Geometry Lesson 1-4 Goal: Measure and Classify Angles Name Hr Pg 28 (3,5,6-10,15-41odd, 53, 54) Show ALL work for credit!!! Learning Target: At the end of today s lesson we will be able to successfully name, measure, and classify angles. An consists of two different rays with the same endpoint. The rays are the of the angle. The endpoint is the of the angle. The angle at the left has sides and The angle can be named,, or. is the vertex of the angle. Example 1: Name the three angles in the diagram below. The Protractor Postulate Consider OB and point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to. The measure of is equal to the between the real numbers for OA and OB.. Angles can be classified as ACUTE, RIGHT, OBTUSE, and STRAIGHT. Example 2: Use the diagram to find the measure of the indicated angle. Then classify the angle. WSR TSW RST VST Example 3: a.) Name all the angles in the diagram below. b.) What type of angles do the x-axis and y-axis form in a coordinate plane?

8 The Angle Addition Postulate If P is in the interior of RST, then the measure of RST is equal to the sum of the measures of and. If P is in the interior of RST, then m RST = m + m Example 4: Given that m GFJ = 155, find m GFH and m HFJ. Example 5: Given that VRS is a right angle, find m VRT and m TRS. Two angles are if they have the same measure. Example 6: a.) Identify all pairs of congruent angles in the diagram. b.) If m P = 120, what is m N? An is a ray that divides an angle into two angles that are congruent. Example 7: In the diagram at the right, WY bisects XWZ, and m XWY = 29. Find m XWZ.

9 Geometry Lesson 1-5: Describe Angle Pair Relationships Name Hr Pg 38 (3-7, 8-28 Even, 29, Even, 46-52) Show ALL work for credit!!! Learning Target: At the end of today s lesson we will be able to successfully use special angle relationships to find angle measures. Each angle is the of each other. Each angle is the of each other. Example 1: a) Given that 1 is a complement of 2 and m 2 = 57, find m 1. b) Given that 3 is a supplement of 4 and m 4 = 41, find m 3. Example 2: The basketball pole forms a pair of supplementary angles with the ground. Find m BCA and m DCA.

10 Example 3: Find m ABC and m CBD for each figure. a.) m ABC = m CBD = b.) m ABC = m CBD = Example 4: a.) Identify each in the figure below. Linear pairs: Vertical angles: b.) Are 1 and 4 a linear pair? Explain why or why not. Example 5: a.) Two angles form a linear pair. The measure of one angle is 3 times the measure of the other. Find the measure of each angle. b.) The measure of an angle is twice the measure of its complement. Find the measure of each angle.

(2) Each side intersects exactly sides, one at each endpoint, so that no two sides with a common endpoint are collinear. The sides of a polygon are the line that form the polygon.

11 !"#$%#"&&'%&%&(%&)%&*%!!"!+ Learning Target: At the end of today s lesson we will be able to successfully classify polygons. VOCABULARY Polygon Sides Vertex Convex Concave A polygon is a plane figure with the following properties: (1) It is formed by three or more line segments called. (2) Each side intersects exactly sides, one at each endpoint, so that no two sides with a common endpoint are collinear. The sides of a polygon are the line that form the polygon. A vertex of a polygon is an of a side of the polygon. A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. A concave polygon is a polygon that is convex n-gon Equilateral Equiangular Regular An n-gon is a polygon with sides. A polygon is equilateral if all of its are congruent. A polygon is equiangular if all of its in the interior are congruent. A polygon is regular if all sides and all angles are.

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13 Name Hr Geometry Lesson 1-7: Find Perimeter, Circumference, and Area Pg (1-3, 4-14 Even, All) Learning Target: At the end of today s lesson we will be able to successfully find dimensions of polygons. Formulas for Area, Perimeter and Circumference: Example 1: The in-bounds portion of a singles tennis court is shown below. Find its perimeter and area. *+,+ Example 2: The smallest circle on an Olympic target is 12 centimeters in diameter. Find the approximate circumference and area of the smallest circle. C = A =

14 Example 3: Find the area and perimeter (or circumference) of the figure. Show ALL formulas used! If necessary round to the nearest tenth.,+,+,+ * + * Example 4: The base of a triangle is 24 feet. Its area is 216 square feet. Find the height of the triangle. Example 5: The area of a triangle is 96 square inches, and its height is 8 inches. Find the length of its base.

Geometry Reasons for Proofs Chapter 1

Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms