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SEMESTER 1 EXAM REVIEW • This review was put together for January 2010. It covers chapters 1-5 and of course emphasizes what I felt was important which may be different from you. Feel free to modify or use as you wish. This will be the class review-and of course it will come with the reward of Jolly Ranchers for correct responses!! • If you have any questions you can ask me-if you can find me!!!! • Diane Bilyeu Chapter 1 True-False • 1. Two points are needed to determine a line. – True A B • 2. Two points are needed to determine a plane – False- a plane needs three points to establish the plane. A B C REFER TO DIAGRAM 1 • • • • • • • 3. NAME 3 COLINEAR POINTS 4. NAME A PLANE 5. NAME THREE NON COLINEAR POINTS 6. NAME TWO LINES ANSWERS 3. CDE 4. T or S 5. Various 6. x, or y, or z True or False • • • • • • 7. A line has two endpoints 8. A segment has two endpoints 9. A ray has two endpoints 10. Identify the figure on diagram 2 A 11. Identify the figure on diagram 2 B 12. The intersection of two lines is a segment. Answers 7. False 8. True 9. False 10. Ray XY 11. Segment LM 12. False A B C 13. If AC is 8, AB is 2, then BC= __________ 14. If AB is 87, BC is 40, then AC = ________ 15. If BC is 104, AC is 214, then AB = ______ 16. What is a “tick mark?” Answers 13. 6 14. 127 15. 110 16. Shows congruence between figures. Naming Angles • A •B C D 17. Name 3 different angles in the diagram. <ABC, <CBD, <ABD Why not <B? Classifying Angles • • • • • • • • Acute, Right, Straight, Obtuse 18. An angle with a measure of 180 degrees 19. An angle with a measure of 90 degrees 20. An angle with a measure of greater than 90 degrees but less than180 degrees 21. An angle with a measure of less than 90 degrees ANSWERS 18. Straight 19. Right 20. Obtuse 21. Acute Angle Measures A • B C D 22. If m <ABC = 42, and the m < CBD = 12, what is the m<ABD?_____________ 23. If the m < ABD is 67, and the m < ABC is 50, what is the m < CBD?________________ 24. If the m<ABD is 87 and the m<CBD is 42, what is the m>ABC?__________________ ANSWERS 22 54 23. 17 24. 45 Chapter 2 A 1. 2. 3. 4. 5. 6. 7. B C If AC = 12, AB = 6, then BC= ____________ If AB = 19, BC=10, then AC= _____________ If AC= 94, BC=18, then AB = _____________ If AB =6x, BC=4x, and AC =200. Solve for x If AB= 14x, BC =24 and AC=20x. Solve for x AC=24. if B is the midpoint, what is AB?___ B is a bisector of AC. If AB=72,and BC is 9x, what is the value of x ANSWERS • • • • • • • • 1. 2. 3. 4. 5. 12-6 = 6 19 + 10 = 29 94-18 = 76 6x + 4x = 200 10x = 200 x=20 14x + 24 = 20x 24 = 6x x=4 6. 12 7. 72 = 9x x=8 Midpoint Formula (55) • 8. Find the midpoint of A ( 1,2) and B (7,4) 1+7 2 4+2 2 8 2 6 2 (4,3) 9. Find the midpoint of C (-2, 3) D (5, -1) 5 + (-2) (-1 + 3) 3 2 ( 3/2, 1) 2 2 2 2 Bisectors • Refer to diagram 3 10. Ray AC bisects<BAD. The measure of m<BAD is 102. What is the measure of <BAC? 11. Ray AC bisects <BAD. m<BAD= 150 degrees and the m< CAD = 10x. Solve for x. ANSWERS 10. ½ X 102 = 51 11. M<CAD= ½ x 150 =10x 75 =10x 7.5 = x Bisectors 12. AC is an angle bisector. m< BAC=60 degrees, m<CAD = 5x. Solve for x. Refer to diagram 4. BC is a bisector of <ABD 13. Solve for x. • ANSWERS • 12. 60 =5x 12=x • 13. 8x + 3 = 9x 3=x Supplementary/Complimentary Angles 14. What is the compliment of a 78 degree angle? 15. What is the supplement of a 129 degree angle? 16. What is the supplement of a 46 degree angle? 17. What is the compliment of a 46 degree angle? ANSWERS 14.12 15. 51 16. 134 17. 44 VERTICAL ANGLES • Refer to diagram 5. • 18. If the m< 1 = 113 find the measures of < 2, <3, <4. • m<2 = 67, m<3 =113, m<4= 67 • 19. If the m<1 = 120 and the m< 4=6x. Solve for x. • 120 + 6x = 180 6x = 60 x=10 Vertical Angles Refer to Diagram 5 • 20. If the m< 4 = 75 and the m<2 =3x. Solve for x. • 75 =3x 25 = x • 21. If the m<3 =97, find the measures of <1, <2, and <4. • m>1 =97, m<2 = 83, m<3 = 83 Angle Measures Refer to diagram 6. 22. Find the measures of the angles. m<1=40, m<2=140, m<3= 40 Refer to diagram 7. 23. Find the measures of the angles. m<1=64, m<2= 93, m<3 =23, m<4 =93 Refer to diagram 8 24.Find the value of x and the measures of the angles. 144+6x =180 6x=36 x=6 m<1=144, m<2=36 Properties of Equality and Congruence • Reflexive Property??? • Symmetric Property???? • Transitive Property???? Chapter 3 • Refer to diagram 9. • 1. Name 2 lines that are parallel • 2. Name 2 lines that are perpendicular • True or false • 3. All right angles are congruent. • 4. If two lines are parallel, then they intersect to form four right angles. • 5. Perpendicular lines form right angles. • 1. c, d 2. b, d 3. True 4. False 5. True Practice • • • • • • • • • • • Refer to page 116 in your book. 6. Do problem 7 X=18 7. Do problem 8 X=6 Refer to page 118 in your book. 8. Do problem 23 -Read directions carefully. x=10, m<CBD =70 Refer to page 120 in your book 9. Do problem 7. x=34 Angles formed by Transversals • • • • • • • Refer to diagram 10. 10. List 4 pairs of corresponding angles. 11. List 2 pairs of alternate interior angles. 12. List 2 pairs of alternate exterior angles. 13. List 2 pairs of same-side interior angles. 14. List 4 pairs of vertical angles. 15. List 2 pairs of supplementary angles. Answers to 10-15 • • • • • • 10. 11. 12. 13. 14. 15. 1+5, 3+7, 2+6, 4+8 3+6, 4+5 1 +8, 2+7, 3+5, 4+6 1+4, 2+3, 5 +8 6+7 5+6, 5+7, 1+3, 2+4, etc….. True or False • • • • • • • • • 16. Corresponding angles are congruent. 17. Same side interior angles are congruent. 18. Alternate exterior angles are congruent. 19. Alternate interior angles are congruent. Refer to page 131 in your book. 20. Do problem 16. 21. Do problem 17. Refer to page 133 in your book. 22. Do problem 33 Answers to 16-22 • • • • • • • 16. 17. 18. 19. 20 21. 22. True False True True x=85 x=104 x=23 Chapter 4 Triangles • • • • • • • • • Equilateral, Isosceles, Scalene 1. A triangle with 2 equal sides_________ 2. A triangle with no equal sides_________ 3. A triangle with 3 equal sides__________ Equiangular, Acute, Obtuse, Right 4. A triangle with all angles less than 90 degrees. 5. A triangle with 1 angle of exactly 90 degrees. 6. A triangle with one angle of over 90 degrees. 7. A triangle with all angles of equal measure (60 degrees) Answers to 1-7 • • • • • • • 1. 2. 3. 4. 5. 6. 7. Isosceles Scalene Equilateral Acute Right Obtuse Equiangular Practice • Refer to page 176 in your book • 8. Do the following problems – – – – – – – – – – – – 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Answers to 11-22 • 8. Do the following problems – – – – – – – – – – – – 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Scalene Isosceles Equilateral Isosceles Scalene Isosceles Acute Acute Right Acute Right Equilateral What is the Triangle Sum Theorem? If you add the measures of the angles of a triangle they total 180 What is the Exterior Angle Theorem? The sum of an interior angle and it’s adjacent exterior angle total 180 • Refer to page 182-183 in your book. • 9. Do the following problems – – – – – 6. 11. 12. 18. 20. Answers to Questions – – – – – 6. 11. 12. 18. 20. 71 45 148 33 x=48, y= 32 True or False • 10. The congruent sides of an isosceles triangle are called the legs. • 11. The third side of an isosceles triangle is called the base. • 12. If two sides of a triangle are congruent, the opposite angles are also congruent. • 13. If two angle of a triangle are congruent the opposite sides are also congruent. True • 14. If a triangle is equilateral it is also equiangular. • ALL ANSWERS ARE TRUE Practice • Refer to page 188-189 in your book. • 15. Do the following problems in your book. Find the value of x – 7. – 9. – 10. – 14. – 18. – 25 ANSWERS TO QUESTIONS – 7. x= 55 – 9. x =45 – 10. x = 7 – 14 5x + 7 = 52 5x =45 x=9 – 18. 80 – 25. 8y – 10 = 4y + 2 4y =12 y=3 What is the Pythagorean Theorem? Leg squared + leg squared = hypotenuse squared What is the Distance Formula? See page 194 • Refer to page 195 in your book. 16. Do the following problems in your book. 8. 10. 14. 15. ANSWERS 8. 15 10. 97 14. 7 15. 80 DISTANCE FORMULA 17. Find the distance between the points A (1, 4 ) B (3, -2) 18. Find the distance between the points C (-2, 2) D (-3, -3) Classifying Triangles Pythagorean Theorem • Refer to chart on page 201 in your book. • Classify the triangles based on the length of their sides. • 19. 4, 6, 7 • 20. 12, 35, 37 • 21. 2, 5, 6 – ANSWERS 19. ACUTE 20. RIGHT 21. OBTUSE Medians of a Triangle • Median of a triangle is a segment from a vertex to the midpoint of the opposite side. • The intersection of the 3 medians of a triangle is called the centroid. The centroid is a point that is 2/3 the distance from the vertex to the opposite side. (see page 208) • Refer to page 209 in your book. • 22. Do the following problems in your book. – – – – 4. 6. 7. PT = 8. BD= ST = ED= ANSWERS TO QUESTIONS – 4. – 6. – 7. – 8. 4 3 PT= 22, ST= 11 BD= 18 ED= 6 Chapter 5 • Refer to diagram 11 • 1. List 3 pairs of congruent angles and 3 pairs of congruent sides. • 2. Write a congruence statement for the two triangles • ANSWERS • 1. D+ T, C+S, E+T, CD=ST, TW=DE, CE=SW • 2. CDE = STW • Refer to diagram 12 • 3. Write a congruence statement for the two triangles. • 4. Why is m<LJK congruent to m< HJG? • 5. Why is m<JLK congruent to m <JGH • ANSWERS • 3. JKL = JHG (VARIOUS) • 4. Vertical angles • 5. Corresponding parts of congruent triangles. Proving Triangles Congruent SSS, SAS, ASA, AAS, HL Identifying Congruent Triangles • Writing a Proof – List the given information first – List the information shown in the diagram – Give a reason for every statement – Use definitions, postulates, theorems etc. – End the proof with what you are trying to prove. L i s Write a two column proof (Refer to diagram 13) • Given: c JL is congruent to NL o L is the midpoint of KM • n Prove: g JKL is congruent to NML r Statement u e 1. JL is congruent to NL n 2. L is the t midpoint to KM 3. <JLK is congruent to <NLM t 4. KL is ocongruent to ML 5. JKLN is congruent to NML M L 6. Page 243 in book. Reason 1. 2. 3. 4. 5. PROOF ANSWERS • Given: JL is congruent to NL • L is the midpoint of KM Prove: JKL is congruent to NML Statement 1. JL is congruent to NL 2. L is the midpoint to KM 3. <JLK is congruent to <NLM 4. KL is congruent to ML 5. JKL is congruent to NML 1. Page 243 in book. Reason 1. Given 2. Given 3. Vertical Angles 4. Def. of midpoint 5. SAS More Proofs • • • • • • • • • • • • Refer to page 247-248 in your book 7. Do problem 34 in the book 8. Do problem 35 in the book 9. Do problem 36 in the book Refer to page 255-256 in your book 10. Do problem 34 in the book 11. Do problem 35 in the book Refer to page 262 in your book 12. Do problem 32 in your book Refer to page 270 in your book 13. Do problem 19 in your book 14. Do problem 20 in your book Using overlapping triangles Refer to page 269 in your book. Sketch triangles separately. 15.Do problem 10 in your book 16.Do problem 17 in your book Set up as a proof. Answers 15.SAS 16.AAS Using Bisectors and Perpendicular Bisectors • • • • • • • • Refer to page 277-278 in your book 17. Do problem 10 in your book 18. Do problem 11 in your book 19. Do problem 14 in your book 20. Do problem 19 in your book Answers 17. 10 19. 38 18. x=6 20. AD= 12, BC = 16