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3 Dear Teacher, lease ensure students know the meaning of all the words used in this booklet including the words pplied cholastics: The word applied means put to use or work. The word scholastics means about learning or school. pplied cholastics means using what you learn. pplied cholastics International was formed to provide educational tools, resources and skills that enable teachers and educators to better fulfill their missions and therefore empower students to live more productive and successful lives. pplied cholastics ntry rogram () is an academic acceleration program specifically structured to repair the holes in a student s education. tudy Guide compiled in booklet form by: pplied cholastics Online cademy 2012 pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities.
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5 Table of Contents Teacher/Tutor Notes 3 tudy Guide 7 Worksheets 17 Worksheet nswers 27 Review 37 Review nswers 41
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7 Teacher/Tutor Notes
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9 Teacher/Tutor Notes ath tudy Guide: Beginning Geometry The following are the key words learned in this tudy Guide: Geometry Ray ine segment nd point Coordinate arallel Intersect erpendicular Diagonal Compass Circumference Radius Chord Diameter rc ngle Vertex Degree rotractor Right angle cute angle Obtuse angle djacent angles Complementary angles upplementary angles Congruent Corresponding angles Hypotenuse egs quilateral Isosceles triangle calene triangle ymmetry Transformation Reflection Rotation Translation The following worksheets are needed for the student to complete this tudy Guide: ines, end points, coordinates & rays Using a compass; circumference, radius, chords, diameter & arc Using a protractor to measure & draw angles Draw & identify different kinds of angles Draw & identify pairs of angles Draw & identify triangles, hypotenuse & legs Identify triangles & angles Identify symmetry & transformations (reflection, rotation, translation) n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 3
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11 tudy Guide
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13 pplied cholastics ntry rogram product of pplied cholastics chievement rogram... For Use with edium/arge class ath tudy Guide Beginning Geometry Your Name: DT: chool: Grade: urpose: To improve your understanding of math words so you can more easily learn and use math. What you will need: ath Glossary; Compass; rotractor tudy Guide: study guide is a lesson that teaches you to learn words and how to do things in an exact order, step by step. Glossary: glossary is a list of words and their meanings in alphabetical order. Twin: twin is a study partner you work with. pplied cholastics: This is the name of the place that wrote the study guide. pplied means put to use or put to work and scholastics means learning or schooling. How to do this study guide: Do each of the steps in this study guide, one at a time, in order and do not skip around. When you finish a step, put your initials and the date on the line on the right. You will be doing worksheets to practice using the math you are learning. The teacher/tutor will check them and help you with any difficulties. split line looks like and means you need to also get an initial from the teacher/tutor when that step is completed. IN 1. DFIN: Find the meaning of the word geometry in the ath Glossary and read it aloud to your twin or teacher/tutor. 2. XRCI: To your twin or teacher/tutor, use the word geometry in sentences until you understand the word. 3. XRCI: earn the following: Different kinds of lines are used to describe shapes and objects. DFIN: Find the meaning of the word ray in the ath Glossary and read it aloud to your twin or teacher/tutor. 4. 7
14 p p l i e d c h o l a s t i c s 5. XRCI: To your twin or teacher/tutor, use the word ray in sentences until you understand the word. 6. DFIN: Find the meaning of the words line segment in the ath Glossary and read it aloud to your twin or teacher/tutor. 7. XRCI: To your twin or teacher/tutor, use the words line segment in sentences until you understand the words. 8. DFIN: Find the meaning of the words end point in the ath Glossary and read it aloud to your twin or teacher/tutor. 9. XRCI: To your twin or teacher/tutor, use the words end point in sentences until you understand the words. 10. DFIN: Find the meaning of the word coordinate in the ath Glossary and read it aloud to your twin or teacher/tutor. 11. XRCI: To your twin or teacher/tutor, use the word coordinate in sentences until you understand the word. 12. XRCI: Use clay or write down on paper to show the teacher/tutor a line segment, ray, end point and coordinate clearly labeled. 13. DFIN: Find the meaning of the word parallel in the ath Glossary and read it aloud to your twin or teacher/tutor. 14. XRCI: To your twin or teacher/tutor, use the word parallel in sentences until you understand the word. 15. DFIN: Find the meaning of the word intersect in the ath Glossary and read it aloud to your twin or teacher/tutor. 16. XRCI: To your twin or teacher/tutor, use the word intersect in sentences until you understand the word. 17. DFIN: Find the meaning of the word perpendicular in the ath Glossary and read it aloud to your twin or teacher/tutor. 18. XRCI: To your twin or teacher/tutor, use the word perpendicular in sentences until you understand the word. 19. DFIN: Find the meaning of the word diagonal in the ath Glossary and read it aloud to your twin or teacher/tutor. 20. XRCI: To your twin or teacher/tutor, use the word diagonal in sentences until you understand the word. 21. XRCI: Use clay or write down on paper to show the teacher/tutor the following types of lines clearly labeled: parallel, intersecting, pependicular and diagonal. 8
15 Be g i n n i n g Ge o m e t r y t u dy Gu i d e 21. XRCI: Do lines worksheet #1. CIRC 1. DFIN: Find the meaning of the word compass in the ath Glossary and read it aloud to your twin or teacher/tutor. 2. XRCI: To your twin or teacher/tutor, use the word compass in sentences until you understand the word. 3. XRCI: ractice using the compass to make circles and parts of circles until you are comfortable using it. 4. DFIN: Find the meaning of the word circumference in the ath Glossary and read it aloud to your twin or teacher/tutor. 5. XRCI: To your twin or teacher/tutor, use the word circumference in sentences until you understand the word. 6. DFIN: Find the meaning of the word radius in the ath Glossary and read it aloud to your twin or teacher/tutor. 7. XRCI: To your twin or teacher/tutor, use the word radius in sentences until you understand the word. 8. DFIN: Find the meaning of the word chord in the ath Glossary and read it aloud to your twin or teacher/tutor. 9. XRCI: To your twin or teacher/tutor, use the word chord in sentences until you understand the word. 10. DFIN: Find the meaning of the word diameter in the ath Glossary and read it aloud to your twin or teacher/tutor. 11. XRCI: To your twin or teacher/tutor, use the word diameter in sentences until you understand the word. 12. DFIN: Find the meaning of the word arc in the ath Glossary and read it aloud to your twin or teacher/tutor. 13. XRCI: To your twin or teacher/tutor, use the word arc in sentences until you understand the word. 14. XRCI: Use clay or write down on paper to show the teacher/tutor the following: circumference, radius, chord, diameter and arc. 15. XRCI: Use a compass to show the teacher/tutor how to draw 3 different sizes of circles. 16. XRCI: Do circles worksheet #2. 9
16 p p l i e d c h o l a s t i c s NG 1. DFIN: Find the meaning of the word angle in the ath Glossary and read it aloud to your twin or teacher/tutor. 2. XRCI: To your twin or teacher/tutor, use the word angle in sentences until you understand the word. 3. DFIN: Find the meaning of the word vertex in the ath Glossary and read it aloud to your twin or teacher/tutor. 4. XRCI: To your twin or teacher/tutor, use the word vertex in sentences until you understand the word. 5. DFIN: Find the meaning of the word degree in the ath Glossary and read it aloud to your twin or teacher/tutor. 6. XRCI: To your twin or teacher/tutor, use the word degree in sentences until you understand the word. 7. XRCI: earn the following rules: circle is 360º. straight line is 180º. 8. DFIN: Find the meaning of the word protractor in the ath Glossary and read it aloud to your twin or teacher/tutor. 9. XRCI: To your twin or teacher/tutor, use the word protractor in sentences until you understand the word. 10. XRCI: ractice using the protractor to make and measure angles until you are comfortable using it. 11. XRCI: Draw a triangle on paper. Use a protractor and show the teacher/tutor how to measure each of the 3 angles. 12. XRCI: Do measuring angles worksheet # DFIN: Find the meaning of the words right angle in the ath Glossary and read it aloud to your twin or teacher/tutor. 14. XRCI: To your twin or teacher/tutor, use the words right angle in sentences until you understand the words. 15. XRCI: earn the following: right angle looks like the corner of a square. Drawing a small square in the corner is a way to name the angle as a right angle. 16. DFIN: Find the meaning of the words acute angle in the ath Glossary and read it aloud to your twin or teacher/tutor. 10
17 Be g i n n i n g Ge o m e t r y t u dy Gu i d e 17. XRCI: To your twin or teacher/tutor, use the words acute angle in sentences until you understand the words. 18. DFIN: Find the meaning of the words obtuse angle in the ath Glossary and read it aloud to your twin or teacher/tutor. 19. XRCI: To your twin or teacher/tutor, use the words obtuse angle in sentences until you understand the words. 20. XRCI: Use a protractor and show the teacher/tutor how to draw each of the following 3 types of angles: right angle, acute angle, obtuse angle. 21. XRCI: Do angles worksheet # DFIN: Find the meaning of the words adjacent angles in the ath Glossary and read it aloud to your twin or teacher/tutor. 23. XRCI: To your twin or teacher/tutor, use the words adjacent angles in sentences until you understand the words. 24. DFIN: Find the meaning of the words complementary angles in the ath Glossary and read it aloud to your twin or teacher/tutor. 25. XRCI: To your twin or teacher/tutor, use the words complementary angles in sentences until you understand the words. 26. DFIN: Find the meaning of the words supplementary angles in the ath Glossary and read it aloud to your twin or teacher/tutor. 27. XRCI: To your twin or teacher/tutor, use the words supplementary angles in sentences until you understand the words. 28. DFIN: Find the meaning of the word congruent in the ath Glossary and read it aloud to your twin or teacher/tutor. 29. XRCI: To your twin or teacher/tutor, use the word congruent in sentences until you understand the word. 30. DFIN: Find the meaning of the words corresponding angles in the ath Glossary and read it aloud to your twin or teacher/tutor. 31. XRCI: To your twin or teacher/tutor, use the words corresponding angles in sentences until you understand the words. 32. XRCI: Use clay or write down on paper to show the teacher/tutor the following types of angles clearly labeled: adjacent angles, complementary angles, supplementary angles and congruent or corresponding angles. 33. XRCI: Do pairs of angles worksheet #5. 11
18 p p l i e d c h o l a s t i c s TRING 1. DFIN: Find the meaning of the word hypotenuse in the ath Glossary and read it aloud to your twin or teacher/tutor. 2. XRCI: To your twin or teacher/tutor, use the word hypotenuse in sentences until you understand the word. 3. DFIN: Find the meaning of the word legs in the ath Glossary and read it aloud to your twin or teacher/tutor. 4. XRCI: To your twin or teacher/tutor, use the word legs in sentences until you understand the word. 5. DFIN: Find the meaning of the word equilateral in the ath Glossary and read it aloud to your twin or teacher/tutor. 6. XRCI: To your twin or teacher/tutor, use the word equilateral in sentences until you understand the word. 7. DFIN: Find the meaning of the words isosceles triangle in the ath Glossary and read it aloud to your twin or teacher/tutor. 8. XRCI: To your twin or teacher/tutor, use the words isosceles triangle in sentences until you understand the words. 9. DFIN: Find the meaning of the words scalene triangle in the ath Glossary and read it aloud to your twin or teacher/tutor. 10. XRCI: To your twin or teacher/tutor, use the words scalene triangle in sentences until you understand the words. 11. XRCI: Use clay or write down on paper to show the teacher/tutor the following clearly labeled: hypotenuse, equilateral, isosceles triangle and scalene triangle. 12. XRCI: earn the following rule: The sum of the 3 angles in all triangles is equal to 180º. 45º + 45º + 90º 13. XRCI: Do triangles worksheet # XRCI: Do angles & triangles worksheet #7. 12
19 Be g i n n i n g Ge o m e t r y t u dy Gu i d e YTRY & TRNFORTION 1. DFIN: Find the meaning of the word symmetry in the ath Glossary and read it aloud to your twin or teacher/tutor. 2. XRCI: To your twin or teacher/tutor, use the word symmetry in sentences until you understand the word. 3. XRCI: earn the following: The dotted line dividing a figure to show the symmetry is called a line of symmetry. 4. XRCI: Use clay or write down on paper to show the teacher/tutor an example of symmetry. 5. DFIN: Find the meaning of the word transformation in the ath Glossary and read it aloud to your twin or teacher/tutor. 6. XRCI: To your twin or teacher/tutor, use the word transformation in sentences until you understand the word. 7. DFIN: Find the meaning of the word reflection in the ath Glossary and read it aloud to your twin or teacher/tutor. 8. XRCI: To your twin or teacher/tutor, use the word reflection in sentences until you understand the word. 9. DFIN: Find the meaning of the word rotation in the ath Glossary and read it aloud to your twin or teacher/tutor. 10. XRCI: To your twin or teacher/tutor, use the word rotation in sentences until you understand the word. 11. DFIN: Find the meaning of the word translation in the ath Glossary and read it aloud to your twin or teacher/tutor. 12. XRCI: To your twin or teacher/tutor, use the word translation in sentences until you understand the word. 13. XRCI: Use clay or write down on paper to show the teacher/tutor the 3 kinds of transformation of a figure. 14. XRCI: Do symmetry & transformation worksheet #8. 13
20 pplied cholastics COTION I have completed this study guide and I understand the words and can do the math problems. tudent: Date: I have taught this student to the best of my ability and he/she has completed this study guide and knows the definitions of the words and can do the math problems. Teacher/Tutor: Date: n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 14
21 Worksheets
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23 Worksheet #1 Name the kind of lines shown. ines ake a number line and circle the coordinates. ake a line segment and circle the end points. Draw a ray. Draw a line segment with coordinates of 7 and 10 as the end points. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 17
24 Worksheet #2 Circles Use a compass and draw a circle. xplain or show where you would find the circumference of it. Use a compass to draw a circle. how a radius. Use a compass to draw a circle. how 2 chords. Use a compass to draw a circle. how a diameter, a radius and an arc. abel each one. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 18
25 Worksheet #3 easuring ngles Use a protractor to measure each angle and write the answer. Use a protractor and draw angles as shown n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 19
26 Worksheet #4 Name the kind of angles shown. ngles Use a protractor and draw a 350 angle. Write down what kind of angle it is. Use a protractor and draw a 1250 angle. Write down what kind of angle it is. Use a protractor and draw a 400 angle. abel the vertex. dd in end points and label them B and C. dd an arc and a ray through its center. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 20
27 Worksheet #5 airs of ngles Name each pair of angles shown Use a protractor and draw supplementary angles. Use a protractor and draw complementary angles. Use a protractor and draw adjacent corresponding angles. Use a protractor and draw two congruent angles. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 21
28 Worksheet #6 Name the kind of triangles shown. Triangles Name the parts of the triangle How many degrees does this angle have? Use a protractor and draw the triangles. equilateral triangle scalene triangle isosceles triangle n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 22
29 Worksheet #7 ngles & Triangles Write the name of each triangle on the line above it. Write the kind of angle shown by the letter on the line below it. C B H F D G J I K N O n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 23
30 Worksheet #8 ymmetry & Transformation C X Draw the line of symmetry for each figure that is symmetrical. R What type of transformation is shown by the moving of these figures? how how to do a translation of this figure. how how to do a reflection of this figure. how how to do a rotation of this figure. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 24
31 Worksheet nswers
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33 Worksheet nswers #1 Name the kind of lines shown. erpendicular ines arallel ake a number line and circle the coordinates ake a line segment and circle the end points. Draw a ray. Diagonal Draw a line segment with coordinates of 7 and 10 as the end points. 4 Intersecting n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 27
34 Worksheet nswers #2 Circles Use a compass and draw a circle. xplain or show where you would find the circumference of it. Use a compass to draw a circle. how a radius. Use a compass to draw a circle. how 2 chords. Use a compass to draw a circle. how a diameter, a radius and an arc. abel each one. s diu Ra rc Diameter n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 28
35 Worksheet nswers #3 easuring ngles Use a protractor to measure each angle and write the answer Use a protractor and draw angles as shown n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 29
36 Worksheet nswers #4 Name the kind of angles shown. right triangle ngles acute angle obtuse angle Use a protractor and draw a 350 angle. Write down what kind of angle it is. acute angle Use a protractor and draw a 1250 angle. Write down what kind of angle it is. obtuse angle Use a protractor and draw a 400 angle. abel the vertex. dd in end points and label them B and C. dd an arc and a ray through its center. B C n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 30
37 Worksheet nswers #5 airs of ngles Name each pair of angles shown adjacent angles complementary angles supplementary angles Use a protractor and draw supplementary angles Use a protractor and draw complementary angles Use a protractor and draw two congruent angles. 900 congruent or corresponding angles Use a protractor and draw adjacent corresponding angles n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 31
38 Worksheet nswers #6 Name the kind of triangles shown. isosceles triangle Triangles equilateral triangle Name the parts of the triangle leg 1. leg 2. scalene triangle How many degrees does this angle have? 3. hypotenuse 900 Use a protractor and draw the triangles. equilateral triangle scalene triangle isosceles triangle n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 32
39 Worksheet nswers #7 ngles & Triangles Write the name of each triangle on the line above it. Write the kind of angle shown by the letter on the line below it. calene triangle Isosceles triangle calene triangle C B right angle acute angle Isosceles triangle Isosceles triangle quilateral triangle F acute angle acute angle calene triangle Isosceles triangle D acute angle obtuse angle calene triangle calene triangle H G acute angle obtuse angle calene triangle quilateral triangle J I K acute angle calene triangle acute angle right angle Isosceles triangle Isosceles triangle N O obtuse angle obtuse angle acute angle acute angle calene triangle acute angle n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 33
40 Worksheet nswers #8 ymmetry & Transformation C X Draw the line of symmetry for each figure that is symmetrical. R What type of transformation is shown by the moving of these figures? reflection rotation translation how how to do a translation of this figure. how how to do a reflection of this figure. how how to do a rotation of this figure. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 34
41 Review
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43 ath Review Beginning Geometry lease write your answers on a separate sheet of paper. You don t need to write the question, just the number. 1. What is geometry? 2. What do you call lines that go along side by side, not getting any closer together or farther apart, as shown here? 3. What is a right angle? 4. Use a protractor to measure the angle. 5. Use a protractor and draw an angle of Draw an obtuse angle. 7. Use a protractor and draw adjacent corresponding angles. 8. Draw a translation of the triangle below. 9. Draw a circle. Draw and label the following: a radius, chord, a diameter and an arc. 10. Name the parts of the triangle below Draw a symmetrical figure with a line of symmetry 12. Name the kind of triangles shown. n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 37
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45 Review nswers
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47 ath Review nswers Beginning Geometry lease write your answers on a separate sheet of paper. You don t need to write the question, just the number. 1. What is geometry? The part of mathematics that describes and measures shapes and objects. 2. What do you call lines that go along side by side, not getting any closer together or farther apart, as shown below? arallel lines 3. What is a right angle? n angle that is 90 degrees (90º) like the corner of a square. 4. Use a protractor to measure the angle Use a protractor and draw an angle of Draw an obtuse angle below. or any obtuse angle 7. Use a protractor and draw adjacent corresponding angles. or any adjacent corresponding angles n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 41
48 ath Review nswers Beginning Geometry 8. Draw a translation of the triangle below. 9. Draw a circle. Draw and label the following: a radius, chord, a diameter and an arc. chord diameter arc radius 10. Name the parts of the triangle below leg 2. leg 3. hypotenuse Draw a symmetrical figure with a line of symmetry or any other correct example 12. Name the kind of triangles shown. isosceles triangle equilateral triangle scalene triangle n pplied cholastics curriculum product pplied cholastics International. ll Rights Reserved. pplied cholastics, pplied cholastics ntry rogram, pplied cholastics chievement rogram and the pplied cholastics open book design are trademarks and service marks owned by ssociation for Better iving and ducation International and are used with its permission. The use of these materials is restricted to pplied cholastics International licensees who are permitted to duplicate and/or translate these documents for use within their licensed group or group activity. ny unauthorized copying, translation, duplication, importation or distribution in whole or in part, by any means, including electronic copying, storage or transmission, is a violation of applicable laws. pplied cholastics International is a non-profit, educational organization and does not discriminate on the basis of race, color, religion, national origin, sex, disability or age in administering student admissions or any of its policies, programs or activities. 42
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