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Unit 1 Review

Unit 1 Review

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Unit 1 Review

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  1. Unit 1 Review Interactive PowerPoint Study Guide for Unit Test 1 Click HERE to go to the topics.

  2. Click to explore Unit 1 Naming and Classifying Divided Line Segments Divided Angles Unit 1 Objectives Angle Relationships Triangles Isosceles and Equilateral Properties For SAT Practice, look on the CCSC website for the SAT PowerPoint from class. For justification practice, look over notes, classwork, and homework. You will be held responsible for everything in the Unit 1 Objectives. For topics not in this PowerPoint, look over notes, classwork, homework, do-nows, and exit tickets.

  3. You should be able to… • name points, lines, line segments, rays, planes, angles, and triangles using names of points. • identify whether a set of given points is collinear. • identify acute, obtuse, right, and straight angles given a diagram or measurement • solve problems about congruent segments and divided or bisected line segments. • solve problems about congruent angles and divided or bisected angles. • solve problems about angle relationships, including vertical and straight angles. • use the fact that angles in a circle add up to 360 to solve problems. • determine the measurement of an angle that is complementary or supplementary to a given angle. There’s more! 

  4. You should be able to… • determine the measurement of an angle that is complementary or supplementary to a given angle • use the triangle sum theorem to solve problems. • Use the exterior angle theorem to solve problems • use properties of angles in isosceles and equilateral triangles to solve problems. • use the “draw a picture and write in everything you know” strategy to solve problems about angles in triangles. • write logical justifications to solutions to geometry problems using the following phrases “it is given that…” “Because [property]…” “Hence,…” and “Therefore [conclusion]” • solve SAT-type problems involving lines, angles, and triangles. Return to Main

  5. Naming and Classifying Overview Click each box to see the label and sketch for each geometric figure. Point • Line • Line Segment Return to Main Next 

  6. Naming and Classifying Overview Click each box to see the label and drawing for each geometric figure. Ray • Angle • Triangle *you should only label angles using one point if there are no other angles sharing the same vertex. Otherwise, use 3 points to label. *careful to label rays starting with the initial point. Return to Main Next 

  7. Classifying Angles Click each box to see the definition and examples of each type of angle. Acute • Right Angles that are greater than but less than Angles that are equal to Obtuse Straight Angles that are greater than but less than Angles that are equal to Return to Main Try some Examples 

  8. Classifying Examples • Use the figure shown to answer the problems. 1. List all of the angles that have S as a vertex. 1. Show Answer 2. Name a straight angle. 2. Show Answer 3. Name an obtuse angle. 3. Show Answer 4. Does appear to be obtuse, straight, right, or acute? 4. Show Answer Acute Return to Main More Examples 

  9. Classifying Examples • Name three collinear points shown in the diagram below. Collinear Points: Points that lie on the same line. A, E, and C or D, E, and B Show Answer Return to Main

  10. Divided Line Segments • Click each box to learn the vocabulary. congruent segments • bisects • midpoint divides a segment into two congruent segments a point that bisects a segment two segments that have the same length. Return to Main Next 

  11. Divided Line Segments • The Segment Addition Postulate: If point B is between A and C, then AB+BC=AC. Also, if AB+BC=AC, then point B is between A and C. AB + BC = AC Return to Main Try Some Examples 

  12. Divided Segments Examples Use the figure below to answer the questions. • If and , what is the length of ? • If and , what is the length of ? Note: Not drawn to scale. Show Answer Show Answer Return to Main More Examples 

  13. Divided Segments Examples Use the figure below to answer the questions. • If , and , find . • If is two more than three times the length of and is 26, what is the length of ? Note: Not drawn to scale. Show Answer Show Answer Return to Main More Examples 

  14. Divided Segments Examples • is the midpoint of . If and , what is the length of • In parallelogram bisects and . If and what is the value of ? Show Answer Show Answer Return to Main

  15. Divided Angles • Click each box to learn the vocabulary. congruent angles • bisects • bisector divides an angle into two congruent angles a ray or segment that bisects an angle two angles that have the same measure. Return to Main Next 

  16. Divided Angles • The Angle Addition Postulate: If ray is on the interior of then . Also, if then ray is on the interior of . Return to Main Try Some Examples 

  17. Divided Angles Examples Show Answer Return to Main More Examples  , Show Answer

  18. Divided Angles Examples • bisects If and then find the values of and the measure of all three angles ( and ) • [Figure not drawn to scale] Show Answer , , Return to Main

  19. Angle Relationships Click each box to see the definition and examples of each angle relationship. Vertical Angles • Linear Pairs Angles that share a vertex and are formed by two pairs of opposite rays. *All vertical angles are congruent* Two angles that share an adjacent side and whose other side is formed by an opposite ray.*The sum of a linear pair is * Complementary Angles Supplementary Angles Two angles whose sum is . Two angles whose sum is Return to Main Try Some Examples 

  20. Angle Relationships Examples • Determine if the following angles are vertical, complementary, or supplementary. Show Answer Show Answer Show Answer vertical supplementary complementary Return to Main More Examples 

  21. Angle Relationship Examples • Refer to the figure to answer the following questions. and and Show Answer Show Answer Show Answer Return to Main More Examples 

  22. Angle Relationship Examples • Use the diagram to answer the questions. Show Answer or Show Answer Return to Main More Examples 

  23. Angle Relationship Examples • Use the diagram to answer the questions. Show Answer Show Answer Return to Main More Examples 

  24. Angle Relationships • Use the diagram shown to answer the question. . If then so is not perpendicular to Show Answer Return to Main

  25. Triangles • The Triangle Sum Theorem: For any triangle, the sum of all interior angles is . . Return to Main Next 

  26. Triangles • The Exterior Angle Theorem: For any triangle, an exterior angle is equal to the sum of the non-adjacent interior angles. Return to Main Next 

  27. Classifying Triangles By Sides: Equilateral: 3 congruent sides Isosceles: 2 congruent sides Scalene: No congruent sides By Angles: Acute triangle: contains 3 acute angles Equiangular triangle: contains 3 congruent angles (must be . Right triangle: contains one right angle Obtuse triangle: contains one obtuse angle Return to Main Try Some Examples 

  28. Triangle Examples • Use the diagram to answer the questions. Show Answer Show Answer Return to Main More Examples  Show Answer

  29. Triangle Examples • Use the diagram shown to answer the questions. Show Answer Return to Main

  30. Isosceles and Equilateral Triangles Equilateral: 3 congruent sides 3 congruent angles () Isosceles: 2 congruent sides (legs) (non-congruent side is the base) 2 congruent angles (base angles) (non-congruent angle is the vertex) Return to Main Try Some Examples 

  31. Examples • Find the value of x in each diagram. Show Answer Show Answer Show Answer Return to Main