Semester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.


 Bruce Owens
 3 years ago
 Views:
Transcription
1 Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No, the three points are not collinear. b. Yes, they lie on the line MP. c. Yes, they lie on the line NP. d. Yes, they lie on the line MO.. Name the plane represented by the front of the box. a. FBC b. BAD c. FEC d. FKG 3. Are points B, J, and C collinear or noncollinear? a. collinear b. noncollinear c. impossible to tell. Name the line and plane shown in the diagram. R U S T a. c. and plane RSU b. line R and plane RSU d. and plane UR and plane UT
2 5. What is the intersection of plane TUYX and plane VUYZ? a. b. c. d.. Name the intersection of plane BPQ and plane CPQ. a. c. b. d. The planes need not intersect. 7. Name a fourth point in plane TUW. a. Y b. Z c. W d. X 8. two points are collinear. a. Any b. Sometimes c. No 9. Plane ABC and plane BCE be the same plane. a. must b. may c. cannot 10. and be coplanar. a. must b. may c. cannot 11. Which diagram shows plane PQR and plane QRS intersecting only in?
3 a. c. b. d. 1. Name the ray in the figure. A B a. b. c. d. 13. Name the ray that is opposite C D B A a. b. c. d. 1. Name the four labeled segments that are skew to
4 a.,,, c.,,, b.,,, d.,,, 15. Name the three labeled segments that are parallel to a.,, b.,, c.,,, d.,, 1. How many pairs of skew lines are shown? a. b. 1 c. 8 d. 17. Which plane is parallel to plane EFHG? a. plane ABDC b. plane ACGE c. plane CDHG d. plane BDHF 18. Find the distance between points P(8, ) and Q(3, 8) to the nearest tenth. a. 11 b. 7.8 c. 1 d The FrostburgTruth bus travels from Frostburg Mall through the City Center to Sojourner Truth Park. The mall is 3 miles west and miles south of the City Center. Truth Park is miles east and 5 miles north of the Center. How far is it from Truth Park to the Mall to the nearest tenth of a mile? a. 9.9 miles b. 3. miles c. 3. miles d.. miles
5 0. A high school soccer team is going to Columbus to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, ) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit. miles.) a. c., 5 miles, 3 miles b., 10 miles d., 1 miles 1. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? y 8 Seaside 8 8 x Landview Oceanfront 8 a. about 10 miles c. about 8 miles b. about 50 miles d. about 0 miles. Find the coordinates of the midpoint of the segment whose endpoints are H(8, ) and K(, 10). a. (7, ) b. (1, ) c. (1, 1) d. (, 8) 3. Find the midpoint of 10 y P x 5 Q 10 a. ( 3, 1) b. (, 0) c. (, 1) d. ( 3, 0)
6 . M(9, 8) is the midpoint of The coordinates of S are (10, 10). What are the coordinates of R? a. (9.5, 9) b. (11, 1) c. (18, 1) d. (8, ) 5. M is the midpoint of for the points C(3, ) and F(9, 8). Find MF. a. 13 b. 13 c. d. 13. Write the two conditional statements that make up the following biconditional. I drink juice if and only if it is breakfast time. a. I drink juice if and only if it is breakfast time. It is breakfast time if and only if I drink juice. b. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice. c. If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time. d. I drink juice. It is breakfast time. 7. One way to show that a statement is NOT a good definition is to find a. a. converse c. biconditional b. conditional d. counterexample 8. Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are congruent, then they have equal measures. and are congruent. a. + = 90 c. is the complement of. b. = d. 9. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. I can go to the concert if I can afford to buy a ticket. I can go to the concert. a. I can afford to buy a ticket. b. I cannot afford to buy the ticket. c. If I can go to the concert, I can afford the ticket. d. not possible 30. Which statement is the Law of Detachment? a. If is a true statement and q is true, then p is true. b. If is a true statement and q is true, then is true. c. If and are true, then is a true statement. d. If is a true statement and p is true, then q is true. 31. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Statement 1: If x = 3, then 3x = 5. Statement : x = 3 a. 3x = 5 c. If 3x = 5, then x = 3. b. x = 3 d. not possible 3. Use the Law of Syllogism to draw a conclusion from the two given statements. If a number is a multiple of,then it is a multiple of 8.
7 If a number is a multiple of 8, then it is a multiple of. a. If a number is a multiple of, then it is a multiple of. b. The number is a multiple of. c. The number is a multiple of 8. d. If a number is not a multiple of, then the number is not a multiple of. 33. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If an elephant weighs more than,000 pounds, then it weighs more than Jill s car. If something weighs more than Jill s car, then it is too heavy for the bridge. Smiley the Elephant weighs,150 pounds. a. Smiley is too heavy for the bridge. b. Smiley weighs more than Jill s car. c. If Smiley weighs more than 000 pounds, then Smiley is too heavy for the bridge. d. If Smiley weighs more than Jill s car, then Smiley is too heavy for the bridge. 3. Which statement is the Law of Syllogism? a. If is a true statement and p is true, then q is true. b. If is a true statement and q is true, then p is true. c. if and are true statements, then is a true statement. d. If and are true statements, then is a true statement. 35. Find the values of x, y, and z. The diagram is not to scale x z y a. c. b. d. 3. Find the value of x. The diagram is not to scale x a. 33 b. 1 c. 17 d Find the value of the variable. The diagram is not to scale.
8 11 x 7 a. b. 19 c. 9 d Find the missing values of the variables. The diagram is not to scale x y 5 a. x = 1, y = 15 c. x = 11, y = 5 b. x = 5, y = 11 d. x = 5, y = Graph y = 3 x 1. a. y c. y x x b. y d. y x x
9 0. Graph. a. y c. 8 8 y 8 8 x x 8 b. 8 y d. 8 y 8 8 x x 8 1. Write an equation in pointslope form of the line through point J( 5, ) with slope. a. c. b. d.. Write an equation in pointslope form of the line through points (, ) and (1, ). Use (, ) as the point (x 1, y 1 ). a. (y ) = (x + ) c. (y + ) = (x ) b. (y ) = (x + ) d. (y + ) = (x ) 3. Write an equation for the horizontal line that contains point E( 3, 1). a. x = 1 b. x = 3 c. y = 1 d. y = 3. Graph the line that goes through point ( 5, 5) with slope 1 5.
10 a. y c. y x x b. y d. y x x 5. Write an equation in slopeintercept form of the line through point P( 10, 1) with slope 5. a. y = 5x 9 c. y 10 = 5(x + 1) b. y 1 = 5(x + 10) d. y = 5x + 1. Write an equation in slopeintercept form of the line through points S( 10, 3) and T( 1, 1). a. 9 x + 13 c. 9 9 x 13 9 b. y = 9 x 13 9 d. y = 9 x Write an equation for the line parallel to y = 7x + 15 that contains P(9, ). a. x + = 7(y 9) c. y = 7(x 9) b. y + = 7(x 9) d. y + = 7(x 9) 8. Is the line through points P(1, 9) and Q(9, ) perpendicular to the line through points R(, 0) and S( 9, 8)? Explain. a. Yes; their slopes have product 1. b. No, their slopes are not opposite reciprocals. c. No; their slopes are not equal. d. Yes; their slopes are equal.
11 9. Write an equation for the line perpendicular to y = x 5 that contains ( 9, ). a. y = (x + 9) c. y 9 = 1 (x + ) b. x = (y + 9) d. y = 1 (x + 9) 50. Are the lines y = x and x + y = 1 perpendicular? Explain. a. Yes; their slopes have product 1. b. No; their slopes are not opposite reciprocals. c. Yes; their slopes are equal. d. No; their slopes are not equal 51. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. 5. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent? a. either ASA or AAS c. AAS only b. ASA only d. neither 53. What else must you know to prove the triangles congruent by ASA? By SAS?
12 ( ( ( A B ( D C a. ; c. ; b. ; d. ; 5. Based on the given information, what can you conclude, and why? Given: I K J H L a. by ASA c. by ASA b. by SAS d. by SAS 55. Find the values of x and y. A y x 7 B D C Drawing not to scale a. c. b. d. 5. Find the value of x. The diagram is not to scale.
13 0 x a. 3 b. 50 c. d The length of G is shown. What other length can you determine for this diagram? D 1 F E a. EF = 1 c. DF = b. DG = 1 d. No other length can be determined. 58. bisects Find FG. The diagram is not to scale. E n + 8 F 3n ) ) D G a. 15 b. 1 c. 19 d Find the center of the circle that you can circumscribe about the triangle.
14 ( 3, 3) 5 y 5 5 x ( 3, ) (1, ) 5 a. ( 1, 1) b. ( 1, 1 ) c. ( 3, 1 ) d. ( 1, ) 0. Where is the center of the largest circle that you could draw inside a given triangle? a. the point of concurrency of the altitudes of the triangle b. the point of concurrency of the perpendicular bisectors of the sides of the triangle c. the point of concurrency of the bisectors of the angles of the triangle d. the point of concurrency of the medians of the triangle 1. Where can the perpendicular bisectors of the sides of a right triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. II only c. I or II only d. I, II, or II. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II 3. In ACE, G is the centroid and BE = 9. Find BG and GE. C B G D A F E a. BG = 1, GE = 3 c. b. d. BG = 1, GE = 1
15 . Name a median for A D E ) ) C F B a. b. c. d. 5. For a triangle, list the respective names of the points of concurrency of perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes. a. incenter circumcenter centroid orthocenter b. circumcenter incenter centroid orthocenter c. circumcenter incenter orthocenter centroid d. incenter circumcenter orthocenter centroid. Where can the lines containing the altitudes of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. I or II only c. III only d. I, II, or II 7. Which diagram shows a point P an equal distance from points A, B, and C? a. c. b. d. 8. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by and is 11 cm, the side included by and is 1 cm, and the side included by and is 1 cm.
16 1 3 a. b. c. d. 9. Name the smallest angle of C The diagram is not to scale. 5 A 7 B a. b. c. Two angles are the same size and smaller than the third. d. 70. Which three lengths can NOT be the lengths of the sides of a triangle? a. 3 m, 17 m, 1 m c. 5 m, 7 m, 8 m b. 11 m, 11 m, 1 m d. 1 m, m, 10 m 71. Two sides of a triangle have lengths 7 and 15. Which inequalities represent the possible lengths for the third side, x? a. c. b. d. 7. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side? a. less than 5 b. less than 10 c. less than 15 d. less than 5 Short Answer 73. Construct the perpendicular bisector of the segment.
17 7. Construct the bisector of 75. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not possible. Explain. Statement 1: If two lines intersect, then they are not parallel. Statement : do not intersect. 7. For the given statements below, write the first statement as a conditional in ifthen form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain. A straight angle has a measure of 180. is a straight angle. 77. Write the missing reasons to complete the flow proof. Given: Prove: are right angles, B A ) D ( C
18 78. Can you conclude the triangles are congruent? Justify your answer. Essay 79. Write a paragraph proof to show that. Given: and B D C A E 80. Write a twocolumn proof. Given: and Prove:
19 B D C A E 81. Write a twocolumn proof: Given: Prove: B C A D Other 8. Use indirect reasoning to explain why a quadrilateral can have no more than three obtuse angles. 83. Keegan knows that the statement if a figure is a rectangle, then it is a square is false, but he thinks the contrapositive is true. Is he correct? Explain. 8. Explain why P, Q, and R are three different points. PQ = 3x +, QR = x, and RP = x +, and.. List the angles of PQR in order from largest to smallest and justify your response. 8. Two sides of a triangle have lengths and 8. What lengths are possible for the third side? Explain.
20 Semester Exam Review Answer Section MULTIPLE CHOICE 1. A. A 3. A. A 5. A. A 7. B 8. A 9. B 10. B 11. C 1. A 13. A 1. A 15. A 1. A 17. A 18. B 19. A 0. C 1. D. A 3. C. D 5. A. B 7. D 8. B 9. D 30. D 31. A 3. A 33. A 3. C 35. D 3. A 37. B 38. C 39. D 0. C
21 1. D. D 3. C. D 5. A. D 7. D 8. B 9. D 50. B 51. B 5. C 53. B 5. A 55. D 5. C 57. A 58. B 59. B 0. C 1. B. A 3. B. D 5. B. C 7. A 8. A 9. D 70. D 71. D 7. A SHORT ANSWER 73.
22 Not possible. Explanations may vary. Sample: To use the Law of Detachment, you must know that the hypothesis is true. 7. If an angle is straight, then its measure is 180. Conclusion: is a. Definition of right triangles b. Converse of Isosceles Triangle Theorem c. Reflexive property d. AngleAngleSide Congruence Theorem 78. Yes, the diagonal segment is congruent to itself, so the triangles are congruent by SAS. ESSAY 79. [] Answers may vary. Sample: You are given that and. Vertical angles BCA and ECD are congruent, so by SAS. [3] correct idea, some details inaccurate [] correct idea, not well organized [1] correct idea, one or more significant steps omitted 80. [] Statement Reason 1. and 1. Given.. Vertical angles are congruent SAS.. CPCTC [3] correct idea, some details inaccurate [] correct idea, not well organized [1] correct idea, one or more significant steps omitted 81. [] Statement 1. and Reason 1. Given.. Reflexive Property ASA.. CPCTC [3] correct idea, some details inaccurate [] correct idea, not well organized
23 [1] correct idea, one or more significant steps omitted OTHER 8. Assume a quadrilateral has more than three obtuse angles. Then it has four angles, each with a measure greater than 90. Their sum is greater than 30, which contradicts the fact that the sum of the measures of the angles of a quadrilateral is 30. Thus a quadrilateral can have no more than three obtuse angles. 83. No; a statement and its contrapositive are equivalent so they have the same truth value. 8. The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. 85. R, Q, P. Sample: Since x = QR > 0, x < x + < 3x +, so QR < RP < PQ. The largest angle ( R) is opposite PQ, the next largest angle ( Q) is opposite RP. 8. Let x be the length of the third side. By the Triangle Inequality Theorem, + x > 8, + 8 > x, and 8 + x >. Solving each inequality, x >, x < 1, and x >, respectively, or < x < 1.
GEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More information5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle  A midsegment of a triangle is a segment that connects
More informationChapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationChapters 6 and 7 Notes: Circles, Locus and Concurrence
Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
More informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationLesson 53: Concurrent Lines, Medians and Altitudes
Playing with bisectors Yesterday we learned some properties of perpendicular bisectors of the sides of triangles, and of triangle angle bisectors. Today we are going to use those skills to construct special
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationCumulative Test. 161 Holt Geometry. Name Date Class
Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationGeometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationChapter 4.1 Parallel Lines and Planes
Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about
More information1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms  These words do not have formal definitions, but there is agreement aboutwhat they mean.
More informationName Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem
Name Period 10/22 11/1 Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle 10/22 Classify and Triangle Angle Theorems
More informationLesson 2: Circles, Chords, Diameters, and Their Relationships
Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct
More informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More informationShow all work for credit. Attach paper as needed to keep work neat & organized.
Geometry Semester 1 Review Part 2 Name Show all work for credit. Attach paper as needed to keep work neat & organized. Determine the reflectional (# of lines and draw them in) and rotational symmetry (order
More information51 Perpendicular and Angle Bisectors
51 Perpendicular and Angle Bisectors Equidistant Distance and Perpendicular Bisectors Theorem Hypothesis Conclusion Perpendicular Bisector Theorem Converse of the Perp. Bisector Theorem Locus Applying
More informationVisualizing Triangle Centers Using Geogebra
Visualizing Triangle Centers Using Geogebra Sanjay Gulati Shri Shankaracharya Vidyalaya, Hudco, Bhilai India http://mathematicsbhilai.blogspot.com/ sanjaybhil@gmail.com ABSTRACT. In this paper, we will
More informationMathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3
Mathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3 The problems in bold are the problems for Test #3. As before, you are allowed to use statements above and all postulates in the proofs
More informationVocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationGeometry. Relationships in Triangles. Unit 5. Name:
Geometry Unit 5 Relationships in Triangles Name: 1 Geometry Chapter 5 Relationships in Triangles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK.
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationLesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each
More informationContents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...
Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................
More informationTerminology: When one line intersects each of two given lines, we call that line a transversal.
Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in the same plane and do not intersect. Terminology: When one line intersects each of two given lines, we call that line a transversal.
More informationGEOMETRY  QUARTER 1 BENCHMARK
Name: Class: _ Date: _ GEOMETRY  QUARTER 1 BENCHMARK Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 1. What is another name
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationHon Geometry Midterm Review
Class: Date: Hon Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 1. Name the plane containing lines m
More informationWeek 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test
Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan
More information2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206  Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
More informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationGPS GEOMETRY Study Guide
GPS GEOMETRY Study Guide Georgia EndOfCourse Tests TABLE OF CONTENTS INTRODUCTION...5 HOW TO USE THE STUDY GUIDE...6 OVERVIEW OF THE EOCT...8 PREPARING FOR THE EOCT...9 Study Skills...9 Time Management...10
More informationCHAPTER 8 QUADRILATERALS. 8.1 Introduction
CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three noncollinear points in pairs, the figure so obtained is
More informationGeometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.
Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.
More informationReasoning and Proof Review Questions
www.ck12.org 1 Reasoning and Proof Review Questions Inductive Reasoning from Patterns 1. What is the next term in the pattern: 1, 4, 9, 16, 25, 36, 49...? (a) 81 (b) 64 (c) 121 (d) 56 2. What is the next
More informationhttp://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4
of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the
More informationDuplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
More informationGeometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
More informationCAIU Geometry  Relationships with Triangles Cifarelli Jordan Shatto
CK12 FOUNDATION CAIU Geometry  Relationships with Triangles Cifarelli Jordan Shatto CK12 Foundation is a nonprofit organization with a mission to reduce the cost of textbook materials for the K12
More informationChapter 5.1 and 5.2 Triangles
Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three noncollinear points are connected by segments. Each
More informationCircle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
More informationIncenter Circumcenter
TRIANGLE: Centers: Incenter Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle. The radius of incircle is
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationMath 531, Exam 1 Information.
Math 531, Exam 1 Information. 9/21/11, LC 310, 9:059:55. Exam 1 will be based on: Sections 1A  1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)
More informationSolutions to Practice Problems
Higher Geometry Final Exam Tues Dec 11, 57:30 pm Practice Problems (1) Know the following definitions, statements of theorems, properties from the notes: congruent, triangle, quadrilateral, isosceles
More informationAdvanced Euclidean Geometry
dvanced Euclidean Geometry What is the center of a triangle? ut what if the triangle is not equilateral?? Circumcenter Equally far from the vertices? P P Points are on the perpendicular bisector of a line
More informationEquation of a Line. Chapter H2. The Gradient of a Line. m AB = Exercise H2 1
Chapter H2 Equation of a Line The Gradient of a Line The gradient of a line is simpl a measure of how steep the line is. It is defined as follows : gradient = vertical horizontal horizontal A B vertical
More informationCK12 Geometry: Parts of Circles and Tangent Lines
CK12 Geometry: Parts of Circles and Tangent Lines Learning Objectives Define circle, center, radius, diameter, chord, tangent, and secant of a circle. Explore the properties of tangent lines and circles.
More informationUnit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook
Unit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook Objectives Identify congruent figures and corresponding parts of closed plane figures. Prove that
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 20072008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 20072008 Pre s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More informationUnit 2  Triangles. Equilateral Triangles
Equilateral Triangles Unit 2  Triangles Equilateral Triangles Overview: Objective: In this activity participants discover properties of equilateral triangles using properties of symmetry. TExES Mathematics
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationalternate interior angles
alternate interior angles two nonadjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects (a description of the location of the angles); alternate
More information3.1 Triangles, Congruence Relations, SAS Hypothesis
Chapter 3 Foundations of Geometry 2 3.1 Triangles, Congruence Relations, SAS Hypothesis Definition 3.1 A triangle is the union of three segments ( called its side), whose end points (called its vertices)
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationNAME DATE PERIOD. Study Guide and Intervention
opyright Glencoe/McGrawHill, a division of he McGrawHill ompanies, Inc. 51 M IO tudy Guide and Intervention isectors, Medians, and ltitudes erpendicular isectors and ngle isectors perpendicular bisector
More informationMathematics Geometry Unit 1 (SAMPLE)
Review the Geometry sample yearlong scope and sequence associated with this unit plan. Mathematics Possible time frame: Unit 1: Introduction to Geometric Concepts, Construction, and Proof 14 days This
More informationCeva s Theorem. Ceva s Theorem. Ceva s Theorem 9/20/2011. MA 341 Topics in Geometry Lecture 11
MA 341 Topics in Geometry Lecture 11 The three lines containing the vertices A, B, and C of ABC and intersecting opposite sides at points L, M, and N, respectively, are concurrent if and only if 2 3 1
More informationPUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS. Middle School and High School
PUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS Length of Course: Elective/Required: Schools: Term Required Middle School and High School Eligibility: Grades 812
More informationQUADRILATERALS CHAPTER 8. (A) Main Concepts and Results
CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More information12. Parallels. Then there exists a line through P parallel to l.
12. Parallels Given one rail of a railroad track, is there always a second rail whose (perpendicular) distance from the first rail is exactly the width across the tires of a train, so that the two rails
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationParallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationSection 91. Basic Terms: Tangents, Arcs and Chords Homework Pages 330331: 118
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
More informationTriangles. Triangle. a. What are other names for triangle ABC?
Triangles Triangle A triangle is a closed figure in a plane consisting of three segments called sides. Any two sides intersect in exactly one point called a vertex. A triangle is named using the capital
More informationThis is a tentative schedule, date may change. Please be sure to write down homework assignments daily.
Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (11) Points, Lines, & Planes Topic: (12) Segment Measure Quiz
More informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationCenters of Triangles Learning Task. Unit 3
Centers of Triangles Learning Task Unit 3 Course Mathematics I: Algebra, Geometry, Statistics Overview This task provides a guided discovery and investigation of the points of concurrency in triangles.
More informationAnalytical Geometry (4)
Analytical Geometry (4) Learning Outcomes and Assessment Standards Learning Outcome 3: Space, shape and measurement Assessment Standard As 3(c) and AS 3(a) The gradient and inclination of a straight line
More informationName: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester
Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester CH. 4 Guided Notes, page 2 4.1 Apply Triangle Sum Properties triangle polygon
More information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationThree Lemmas in Geometry
Winter amp 2010 Three Lemmas in Geometry Yufei Zhao Three Lemmas in Geometry Yufei Zhao Massachusetts Institute of Technology yufei.zhao@gmail.com 1 iameter of incircle T Lemma 1. Let the incircle of triangle
More informationA summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of midpoint and segment bisector M If a line intersects another line segment
More informationThe common ratio in (ii) is called the scaledfactor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1
47 Similar Triangles An overhead projector forms an image on the screen which has the same shape as the image on the transparency but with the size altered. Two figures that have the same shape but not
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationLesson 18: Looking More Carefully at Parallel Lines
Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180. They learn how to prove the alternate interior angles theorem using
More informationThe Triangle and its Properties
THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three
More informationPOTENTIAL REASONS: Definition of Congruence: Definition of Midpoint: Definition of Angle Bisector:
Sec 1.6 CC Geometry Triangle Proofs Name: POTENTIAL REASONS: Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. Definition of Midpoint: The point
More information