Name Date Period. 1.1 Understanding the Undefined Terms
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1 Name Date Period Lesson Objective: 1.1 Understanding the Undefined Terms Naming Points, Lines, and Planes Point Line Plane Collinear: Coplanar: 1. Give 2 other names for PQ and plane R. 2. Name 3 points that are collinear and 3 points that are coplanar. Using Defined Terms: Defined terms are terms that can be described using words such as: or The definitions below use AB shown here: Vocab Term Definition Diagram Name Segment Ray
2 Vocab Term Definition Diagram Name Opposite Rays 3. Give another name for GH. 4. Name all rays with endpoint J. 5. Which of the rays from #4 are opposite rays? Sketching Intersections Two or more geometric figures intersect if What about lines and planes? 1. Sketch a plane and a line that is in the plane. 2. Sketch a plane and a line that does not intersect the plane. 3. Sketch a plane and a line that intersects the plant at a point. 4. Sketch two different lines that intersect the plane at the same point. Think About It look back to #8 and #9. Do those lines lie in the same plane as the one drawn? Explain.
3 Name Date Period Lesson Objective: 1.2 Measuring Segments Finding the distance between two points on a number line is relatively trivial, which means it is something that we accept without much proof needed to verify. This is what we call a or an in Geometry. Ruler Postulate: The distance between 2 points is the of the of the two coordinates. Example: 1. Measure the length of MN to the nearest tenth of a centimeter. Congruent Segments Line segments that have the length are called. LENGTHS are Equal SEGMENTS are Congruent Example: 2. Plot J(-3, 4), K(2, 4), L(1, 3) and M(1, -2) in the coordinate plane below. Then determine whether JK and LM are congruent.
4 Using the Segment Addition Postulate Think About It How far is Sacramento from San Bernadino? Briefly explain how your group found the answer. **When three points are collinear, we can say that one point is the other two. Segment Addition Postulate: If B is between A and C, then. 3. Find DF. (*remember, no bar on top of DF means find its ) 4. Find GH. 5. How far is Tulsa from St. Louis? Think About It In the diagram, WY = 30. Can you use the Segment Addition Postulate with the other given lengths to find the distance between points W and Z? Briefly explain why this is or is not possible.
5 Name Date Period Lesson Objective: 1.3 Measuring Segments // Midpoint and Distance in the Coordinate Plane Midpoints and Segment Bisectors Midpoint: The midpoint of a segment is the point that divides the segment into. Segment Bisector: A segment bisector is a that intersects the segment at its. 1. Make a sketch of the following phrase: VW bisects XY at point T Identify the segment bisector of PQ. Then find PQ. Using Algebra with Segment Lengths Example: 4. Point M is the midpoint of VW. Find the length of VM.
6 Using the Midpoint Formula The Midpoint Formula: The coordinates of the midpoint of a segment are the of the x- coordinates and the of the y-coordinates of the endpoints. 5. The endpoints of RS are shown in the diagram. Find the coordinates of the midpoint M. 6. The midpoint of JK and endpoint J are given. Find the coordinates of the other endpoint, K. The Distance Formula: If A(, ) and B(, ) are points in the coordinate plane, then the distance between A and B is: Example: 7. Find the distance between R(2, 3) and S(4, -1). Make a sketch on the coordinate plane provided.
7 Name Date Period 1.4 Perimeter and Area in the Coordinate Plane Lesson Objective: Polygons Polygon; A polygon is a closed, plane figure formed by line segments called. Classifying Polygons There are two different kinds of polygons, and String Test: Imagine a string wrapped around the polygon If there is a gap between the string and a polygon, it is. If there is NOT a gap between the string and a polygon, it is. Example: 1. First, name the polygon by the number of sides it has. Then classify the polygons using the vocab terms above. a. b. Perimeter (P) and Area (A) Triangle Square Rectangle Finding Perimeter in the Coordinate Plane Example: 2. Find the perimeter of ΔABC with vertices A(-2, 3), B(3, -3) and C(-2, -3).
8 Finding Area in the Coordinate Plane Example: 3. Find the area of ΔDEF with vertices D(1, 3), E(4, -3) and F(-4, -3) HW # : Complete the following on a separate sheet of graph paper. Classify the polygon by the number of sides. Tell whether it is convex or concave. Use the diagram below to complete the following:
9 Name Date Period Lesson Objective 1.5 Measuring Angles Naming Angles Angle: An angle is a set of points consisting of that have the same, called the. The are the of the angle. ***If more than one angle has the save vertex, the name (vertex point) cannot be used!!! Example: 1. A lighthouse keeper measures the angles formed by the lighthouse at point M and 3 boats. Name 3 angles in the diagram. Measuring Angles Protractor Postulate: The measure of AOB ( ) is equal to the difference between the real numbers matched with OA and OB. Classifying Angles Acute Angle Right Angle Obtuse Angle Straight Angle
10 Example: 2. Find the measure of each angle. Then classify each angle. a. GHK b. JHL c. LHK Identifying Congruent Angles Congruent Angles: Two angles are congruent when they have the. MEASURES of angles are EQUAL Example: 3. Find m ABC. 4. m RST = 114. Find m RSV. 5. L is in the interior of JKM. Find m LKM if m JKL = 56.4 and m JKM = Sketch a diagram first
11 Name Date Period 1.6 Describing Pairs of Angles Lesson Objective: Complementary and Supplementary Angles Adjacent Angles: Two angles that share a and, but NO common. Complementary Angles: Two positive angles whose measures have a of. Supplementary Angles: Two positive angles whose measures have a of. **Complementary and supplementary angles can be adjacent or nonadjacent angles. 1. Name a pair of complementary angles. 2. Name a pair of supplementary angles. 3. Name a pair of adjacent angles. Think About It Are FGK and KGH adjacent angles? Why or why not? Are KGH and LKG adjacent angles? Why or why not? Are FGK and FGH adjacent angles? Why or why not?
12 4. 1 is the complement of 2. m 1 = 62. Find m 2. Draw a diagram is the supplement of 4. m 4 = 47. Find m 3. Draw a diagram. Using Algebra with Complementary, Supplementary, and Adjacent Angles 6. LMN and PQR are complementary angles. Find the measures of the angles when m LMN = (4x 2) and m PQR = (9x + 1) and 2 are supplementary angles. Find the measures of the angles when m 1 = (7x + 13) and m 2 = (25x + 7) 8. When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find m BCE and m ECD.
13 Name Date Period Lesson Objective: 1.6 Describing Pairs of Angles (continued) Linear Pairs and Vertical Angles Linear Pair: Two angles are a linear pair when their sides are. Think About It What can we conclude about the sum of 3 and 4? Briefly explain your group s reasoning. Vertical Angles: Two angles are vertical angles when their sides form two pairs of 1. Name all the linear pairs in the diagram. 2. Name all the vertical angles in the diagram. 3. Two angles form a linear pair. The measure of one angle is five times the measure of the other angle. Find the measure of each angle. Draw a diagram. 4. The measure of an angle is 9 times the measure of its complement. Find the measure of each angle. Draw a diagram.
14 5. Two angles form a linear pair. The measure of one angle is 1.5 times the measure of the other angle. Find the measure of each angle. 6. Do any of the numbered angles form a linear pair? Briefly explain your reasoning. 7. Which angles are vertical angles? What can we conclude from JUST the diagram? For any diagram, there are some things you can conclude, and some that you cannot. Quickly brainstorm with your group what you think you CAN conclude about the diagram below: What we CAN conclude: What we CANNOT conclude:
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