Geometry Review for Semester 1 Final Exam

Transcription

1 Name Class Test Date POINTS, LINES & PLANES: Geometry Review for Semester 1 Final Exam Use the diagram at the right for Exercises 1 3. Note that in this diagram ST plane at T. The point S is not contained in the plane. intersects the 1. Name two opposite rays in the diagram. 2. Identify 3 collinear points and 4 non-coplanar points. 3. Name the plane 3 different ways. Why is plane LTX not a correct name for the plane? MEASURING SEGMENTS AND ANGLES: Use the figure for Exercises Name a segment congruent to GJ. 5. Name the coordinate of the midpoint of NH. In the diagrams below, identify the relationship of angles shown, and then find the value of each variable and the measure of each angle. 6. a. b. 7. a. b. 8. Find the value of x. 9. Assume that Q is the midpoint of PR. Find x, PQ, QR, and PR. PQ = 3x + 7, QR = 5x 19

2 ANGLE PAIRS: Use the figure at the right for Exercises Name a pair of vertical angles. 11. Name a pair of adjacent angles with vertex L. 12. Name a linear pair and 2 are supplementary angles. m 1 is 4y + 7 and m 2 is 9y + 4. What is m 2? PATTERNS & CONJECTURES Find a pattern for each sequence. Describe the pattern and find the next two terms of each sequence , 1, 7, 0, 9, 1, 11, , -36, 216, -1296, 7776, Find a counterexample to show that each conjecture is false. 16. An apple is a red fruit. 17. If a parallelogram has four congruent sides, then it is a square. CONDITIONAL STATEMENTS: Write the converse, inverse, and contrapositive of the given conditional. Determine the truth value of each statement. 18. If a polygon is a triangle, then it has exactly three sides. Converse: Inverse: Contrapositive: Biconditional (if possible): 19. If Jerrod is in 11th grade, then Jerrod is in high school. Converse: Inverse: Contrapositive: Biconditional (if possible): PROVING ANGLES CONGRUENT: Use the diagram at the right for Exercises Find x. 21. Find m AEC. 22. Find m CED.

3 REASONING PROPERTIES: Name the property that justifies each statement. 23. m ABC = m DEF and m DEF = m ABC 24. AB = CD, CD = EF. Therefore, AB = EF. 25. MB MB ANGLES RELATIONSHIPS IN TRIANGLES: 26. Find the missing angle in the triangle below. 27. Find the value of the variables in the triangle at the right. PROPERTIES OF PARALLEL LINES: For Exercises 27-31, suppose a b and c d and 10 are what kind of angles? and what angle are alternate interior angles? 30. Which angle could you show is congruent to 11 to prove a b? 31. If m 6 50, then find m If m 1 130, then find m 5. EQUATIONS OF LINES: 33. Find the slope of the line passing through ( 6, 2) and ( 3, 6). 34. Find the equation of the line with a slope 6 and y-intercept Find the equation of the line passing through (10, 2) and (2, 2).

4 PARALLEL & PERPENDICULAR LINES: Determine whether the following pairs of lines are parallel, perpendicular, or neither. 36. y = 2x + 1 2x + y = 7 2y = 3x 6 y = 3 x + 5y = 15 2 x y + 4 = 5x 37. What is the equation of the line parallel to y = x 1 that contains the point (1, 2)? 38. What is the equation of the line perpendicular to y = 1 x + 1 that contains the point ( 2, 1)? 2 CONGRUENT FIGURES: 39. If CDEF KLMN, what are the congruent corresponding parts (list all sides and angles)? 40. If ΔUVW ΔEFC, what is the measure of FEC? CONGRUENT TRIANGLES: 41. State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot be proven congruent, write not enough information. a. b. c. d. e. f.

5 42. Complete the proof. Given: YA BA, B Y Prove: AZ AC Statements Reasons 1) YA BA, B Y 1) 2) are vertical angles. 2) Definition of vertical angles 3) YAZ BAC 3) 4) 4) 5) 5) CPCTC ISOSCELES AND EQUILATERAL TRIANGLES: 43. Find the value of x and y. a. b. 44. Complete the proof. Given: XY XZ, and XB is the angle bisector of X. Prove: XB YZ Statements Reasons 1) XY XZ, XB is the angle bisector of X. 1) 2) 2) Definition of angle bisector. 3) XB XB 3) 4) XYB ΔXZB 4) 5) 4 5 5) 6) m 4 m 5 = 180 6) 7) 2( m 4 ) = 180 7) Substitution Property of 8) m 4 = 90 8) 9) 9) DISTANCE AND MIDPOINT: 45. What is the distance between points M(6, 16) and Z( 1, 14) to the nearest tenth? 46. What is the midpoint between (-2, 0) and (-5, 2)? 47. The midpoint of GN is (9, 11). One endpoint is N(7, 5). Your friend calculates the coordinates of endpoint G as (16, 16). Is he correct? If not, what is his error?

6 MIDSEGMENTS OF TRIANGLES 48. What is the value of x in the triangles at right? 49. What is the perimeter of FGE? 50. What is a rule that describes the translation that maps QRST onto Q'R'S'T' in the figure at right? 51. ABC has vertices A( 2, 0), B(2, 5), and C(3, 1). The image of ABC following a reflection is A'B'C' with vertices A' ( 2, 0), B' (2, 5) and C' (3, 1). What is a rule that describes the reflection? 52. Graph the images. 53. Triangle RST has vertices R( 2, 2), S(1, 1), and T( 1, 3). Find the coordinates of the image of each vertex for the given translation. a. (x, y) (x 4, y + 3) b. Triangle RST translated 1 unit to the left and 2 units up 54. Find the image of each figure for the given dilation. Is the image a reduction or enlargement? a. L(6, 4), P(3, 5), Q(1, 1); scale factor of 1.2 b. S( 2, 6), T(8, 4); scale factor of 1 4 c. W( 3, 2); scale factor of Determine the scale factor from the following image and pre-image. a. A(2,3), B(5,10) b. C(16,4), D(3,6), E(26,1) A (6,9), B (15, 30) C (8,2), D (1.5, 3), E (13,.5)

7 Vocabulary Terms: The following are geometry terms we have studied this semester. Most of them are covered in the problems in the review packet. Topic 8: Transformational Geometry: Congruent Dilation Enlargement Image Line of reflection Line of symmetry Preimage Reduction Reflection Reflectional Symmetry Rigid Transformation Rotation Rotational Symmetry Scale factor of a dilation Transformation Translation Topic 4: Congruent Triangles: Base of an Isosceles Triangle Base Angles of an Isosceles triangle Congruent Polygons Hypotenuse Legs of a right triangle Legs of an isosceles Triangle Vertex angle of an Isosceles triangle Side-Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Angle-Angle-Side (AAS) Hypotenuse-Leg (HL) Corresponding Parts Topic 1: Tools of Geometry Acute Angle Obtuse Angle Straight Angle Right Angle Adjacent Angles Angle Angle Bisector Collinear Points Complementary Angles Congruent Angles Congruent segments Coplanar Intersection Linear pair Midpoint Perpendicular bisector Perpendicular lines Point Line Plane Ray Opposite rays Segment Segment bisector Space Supplementary angles Vertex of an angle Vertical angles Topic 5: Relationships Within Triangles Distance Formula Distance of a segment Midsegment of a triangle Midpoint Formula Midpoint of a segment Coordinates of a point Topic 2: Reasoning & Proof Biconditional Conclusion Conditional Conjecture Contrapositive Converse Counterexample Deductive reasoning Hypothesis Inductive Reasoning Inverse Negation Proof Symmetric Property Reflexive Property Theorem Transitive Property Truth Value Topic 3: Parallel & Perpendicular Lines Alternative Exterior Angles Alternate interior angles Corresponding angles Euclidean Geometry Exterior Angle of a polygon Parallel lines Parallel planes Perpendicular Bisector Point-Slope form Remote interior angles Same-side interior angles Skew lines Slope Slope-intercept form Transversal line