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Name _____________________ Algebra & Geometry Review Geometry Topic 1 Language of Geometry PROBLEM PACKET Algebra & Geometry Review Geometry Topic 1 Problem Packet 1 Homework Assignments!! Assignment Number Description of Assignment Algebra & Geometry Review Date Assigned Geometry Topic 1 Problem Packet Date Due 2 1.1 Mathematical Word Roots The definitions of many words in geometry are directly related to their word roots. 1. Pentagon – Word Root 1: PENTA meaning five, Word Root 2: GONIA meaning angle Definition of Pentagon: a five sided figure (has five angles too) 2. Concentric – Word Root 1: CON meaning with or same, Word Root 2: CENTRE meaning center Definition of Concentric : Concentric circles have the same center Directions: Complete the table by finding the one or two Latin/Greek roots, their meaning, and the definition of each geometry term in the table. Use your notes! Geometry Term Root 1 Meaning Root 2 Meaning Definition of Geometry Term Polygon Trisect Quadrilateral Triangle Isosceles Circumference Hemisphere Intersect Rectangle Bisect Collinear Sesquicentennial* Democracy* Calorie* *These words aren’t directly related to geometry. See if you can break them down into their roots. Use the Internet if you need help. Algebra & Geometry Review Geometry Topic 1 Problem Packet 3 1.2 Points, Lines, and Planes Geometry is based on the fact that points, lines, and planes have no definitions. It is upon these words that the basic structures of geometry are built. Each of these structures has a unique way in which we write them. Consider the following example: Some examples from the diagram to the right: 1. 3 points: J, A, and K sur 2. A line containing H and I: HI 3. A plane: plane GHI 4. A segment with K and G as endpoints: KG 5. A ray starting at A and passing uur through J: AJ Directions: For #1 – 6, write each of the following using the appropriate symbols: 1. The segment with endpoints T and S 2. The ray that begins at R and passes through P 3. 4. 5. 6. 7. Draw a line that passes through A, B, and C. Name it using appropriate symbols. 8. Draw a line segment and name it two different ways. Algebra & Geometry Review Geometry Topic 1 Problem Packet 4 1.2 Points, Lines, and Planes (cont.) Directions: For #9 – 12, sketch the following: uur 9. Draw ST 10. Draw AB 11. Draw J suur 12. Draw NB Directions: For #13 – 22 refer to the picture to the right. 13. 14. 15. 16. 17. 18. 19. 20. Name four points. Name three lines. Name three rays. Name two segments that contain I. Name two lines that contain J. Name a plane. Name the point that is between J and I. Name the point that is common to three lines. 21. Name three non-collinear points. 22. Name three collinear points. 23. Use the idea of a line segment to describe a triangle. 24. Use the idea of a line segment to describe a six-sided figure. suur suur suur 25. Draw a figure with points B, C, D, E, F, and G that shows lines CD , BG , and EF , with C on all three lines. Directions: For #26 – 28, how many different lines can you create that contain at least 2 points? 26. 27. 28. Algebra & Geometry Review Geometry Topic 1 Problem Packet 5 1.3 Naming Angles Angles have different parts and we name them in a certain way: The sides of an angle are the two uuur uuuur rays that intersect: DG and DM are the sides of this angle The vertex of an angle is the point where the two sides meet: D is the vertex of this angle You name an angle using three points where the vertex of the angle must go in the middle: This angle is called ÐGDM or ÐMDG . Sometimes angles are numbered and it’s OK to use that number. We can also call this angle Ð1. Part I: Place a word from the list below in each of the blank spaces in the paragraph. (Each word is used only once.) Vertex Sides Three Rays Vertex Angle Vertex An _______________________ is formed when two rays meet at their endpoints. The two _________________ that intersect to form an angle are called the _________________ of the angle. The endpoint where the two rays intersect is called the ______________________ of the angle. An angle is named using ____________________ points: one point on one of its sides, then the ______________________, and a point on the other side. The ____________________ is always the second point used to name the angle. Part 2: Draw the following angles: 1. ÐTVE 2. ÐTEV 3. ÐETV 4. For the angle in question 3, how many different ways could you correctly name it? Algebra & Geometry Review Geometry Topic 1 Problem Packet 6 1.3 Naming Angles (cont.) Part III. Name the numbered angles in each drawing. 5. 6. 7. 8. 9. Algebra & Geometry Review Geometry Topic 1 Problem Packet 7 1.4 Midpoints and Bisectors A midpoint is a point that cuts a line segment into two congruent parts. A bisector is a more general term for a ray, line, or line segment that divides something else into 2 congruent parts. uuur Ex: Suppose AB bisects Ex: Suppose M is the midpoint ÐCAD . If mÐCAD = 60o , then, mÐCAB = mÐBAD = 30o of AB . If AB = 6 cm, then AM = MB = 3cm 1. Explain what a midpoint is. Draw a diagram that contains a midpoint and mark it appropriately to show that the point you drew is actually a midpoint. 2. Explain what a segment bisector is. 3. Explain what an angle bisector is. Directions: For #4 – 7, sketch the following pictures and be sure to mark them appropriately. 4. AB bisects CD uuur 5. HK bisects ÐPHR 6. M is the midpoint of TV suur 7. GH bisects BX at H Directions: For #8 – 14, answer the following questions based on this diagram. 8. Name a ray 9. Name a line 10. Name a segment 11. Name the segment bisector 12. Name a midpoint 13. Name a point that is not a midpoint 14. Name an angle Algebra & Geometry Review Geometry Topic 1 Problem Packet 8 1.4 Midpoints and Bisectors (cont.) Directions: For #15 – 18, answer the following questions based on this diagram. 15. 16. 17. 18. Name the angle bisector Name the angle that is being bisected What is mÐTPK ? What is P called? We sometimes want to describe points that are not necessarily midpoints. The segment addition postulate says that if C is a point on AB , then AC + CB = AB Ex: Since AC+ CB = AB, we know that AB = 7 cm. 19. If C is a point on AB and AC = 3 in and CB = 1.5 cm, find AB. 20. If C is a point on AB and AB = 12 mm, and AC = 8 mm, find CB. 21. If E is a point on DF and DE = x + 2, EF = 8, and DF = 15, find the value of x. 22. If E is a point on DF and DE = 3x and, EF = 6, and DF = 24, find DE. Algebra & Geometry Review Geometry Topic 1 Problem Packet 9 Algebra & Geometry Review Geometry Topic 1 Problem Packet 10