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Transcript
Unit 1: Foundations of Geometry Name: ___________________________ Hour: ___ 1.1 Understanding Points, Lines, and Planes Vocabulary Point: Line: Line Segment: Ray: Opposite Ray: Endpoint: Plane: Collinear: Coplanar: Whole Class Examples: Follow the directions for the problems below. 1. Answer the following questions below: a) How many points must exist in order to make a line? b) How many points must exist in order to make a plane? Must they be collinear? c) How many intersection points occur when two lines intersect? d) When two planes intersect what do they form? 2. Draw an example of the following situations a) Segment DC b) E, F, G, H are coplanar points c) Line R, S 3. a) Name four coplanar points using the figure to the right b) Name two opposite rays (add a reference point if needed) c) Name four lines in the figure to the right 4. Write and draw Real-Life Examples of the following terms 1. Point 2. Line 3 Plane 4. Segment 6. Ray 5. Endpoint Practice: Follow the directions for the problems below. 1. What does undefined mean? a) Which terms above do you feel are undefinable? 2. a) Name a set of non-collinear points b) Name a ray c) Name a segment 3. What is the greatest number of intersection points 4 coplanar lines can have? Draw an example. a) 0 b) 2 c) 4 d) 6 4. Line AB = Line BA true or false? Draw an example. Think About The Situation (TATS): Sometimes, always, never: If two rays share a common endpoint then they form a line? Draw an example to support your answer. 1.2 Measuring and Constructing Segments Vocabulary Distance Length Midpoint Congruent Congruent Segments Bisect Segment Bisector Construction Segment Addition Postulate Constructions: 1. Constructing Congruent Segments: 2. Bisecting a Segment: 3. Whole Class Examples: B is between C and E. πΆπΈ = 17.1 and π·πΈ = 8, find CD. B is the midpoint of AC, if AB = 10 what is the length of AC? AC and CF are congruent. If π΄πΆ = 10, and πΆπΉ = 2π₯ what is the value of x? Practice: Follow the directions for the problems below. 1. M is between N and O. Find NO. 2. D is the midpoint of EF, ED = 4x + 6, and DF = 7x β 9. Find ED, DF, and EF. 3. If π΄π΅ = 10 ππ, place point C so that it is ¾ ππ π΄π΅. Think About The Situation (TATS): Explain the followingβ¦ 1. Suppose R is the midpoint of ST, explain how SR and ST are related. Diagram this. 2. How are drawing and constructing similar? How are they different? 1.3 Measuring and Constructing Angles Vocabulary Angle (vertex, interior, exterior) Measure Degree Congruent Angles Acute Angle Angle Bisector Right Angle Angle Addition Postulate Constructions: 1. Constructing Congruent Angles: 2. Bisecting an Angle: Obtuse Angle Straight Angle 3. Whole Class Examples: Ray ST bisects β πΎππ. If β πΎππ = 75, what is the measure of β πΎππ? If πβ π·πΈπΉ = 48° and πβ πΉπΈπΊ = 67°, Find πβ π·πΈπΊ Angles XYW and WYZ form a complementary angle. If πβ πππ = 2π₯ & π β πππ = 3π₯ find the value of x. Practice: Follow the directions for the problems below. 1. Angles XYW and WYZ form a linear pair. If πβ πππ = 2π₯ β 5 and π β πππ = 3π₯ + 10 find the value of x. 2. If πβ πππ = 5π₯ + 20° and πβ πππ = 3π₯ + 10° and πβ πππ = π₯ + 30. 4. KM bisects β π½πΎπΏ, πβ π½πΎπ = (4π₯ + 6) °, and πβ ππΎπΏ = (7π₯ β 12) °. Find πβ π½πΎπ. Think About The Situation (TATS): Explain the followingβ¦ 1. The measure of an obtuse angle is 5x + 45 what is the largest value for x? 1.4 Pairs of Angles Vocabulary Adjacent Angles Linear Pair Complementary Angle Supplementary Angles Vertical Angles Whole Class Examples: Follow the directions for the problems below. 1. Draw an example of the following situations a) Right Angle ABC b) Complementary angles RST and UVX c) Lines AB and CD intersect at point E to form vertical angles 1, 2, 3, and 4. 2. Use the figure to the right. a) Give an example of an acute angle b) Give an example of vertical angles c) Give a set of angles that form a linear pair 3. Write and draw Real-Life Examples of the following terms 1. Adjacent Angles 2. Linear Pair 3. Vertical Angles 4. Complementary Angles 5. Supplementary Angles 6. Straight Angle Practice: Follow the directions for the problems below. 1. How does the definition of βadjacentβ help us in defining adjacent angles? a) Can you use the same method in defining any other vocabulary terms from above? 2. Find the value of the variable below. a) Find the complement of (7π₯ β 12)°. Find the supplement. b) π΄ππππ π΄ = 7π₯ + 10 and π΄ππππ π΅ ππ 31, find the value of x. Think About The Situation (TATS): True or false, if false explain whyβ¦ 1. A pair of vertical angles may also form a linear pair. 2. If an angle is acute then its complement should be greater than its supplement. 1.6 Midpoint and Distance in the Coordinate Plane Vocabulary Coordinate Plane Midpoint Formula Right Triangle (legs and hypotenuse) Pythagorean Theorem Midpoint Examples: Follow the directions for the problems below. 1. Calculate the midpoint of the following segments shown on the graphs below. Write your answer as an ordered pair. a. b. c. 2. Solve the following midpoint problems below. a. What is the other endpoint of a segment if one endpoint is at (2, 5) and its midpoint is at (5, 1)? b. What is the ordered pair of the point that is one-forth of the way from (2, 4) to (10,8)? Distance Examples: Follow the directions for the problems below. 1. Calculate the distance of the segments in the graphs below. a. b. c. 2. Solve the following distance problems below. a. What is the distance of a segment with endpoints (0, -2) and (-5, -1)? b. If a segment begins at (-2, 2) and is 7 units long, what are four possible coordinates for its other endpoint? c. The four bases on a baseball field form a square with 90ft sides. The center of the pitching mound has coordinates (42.8, 42.8). When a pitcher throws from the center of the mound to home plate, what is the distance of the throw, to the nearest tenth?