geometry(semester(1exam(review( 1=(15x tqm?( x m 1?(
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Geometry Semester 1 Exam Review 1. Two lines intersect as shown. What is the value of x?
2. In this figure, m∠1=(15x−5)° and m∠2=(10x+35)°. What is m∠1?
3. What is m∠TQM?
4. In this figure, line t is a transversal of lines m and n. Which of the following statements determines that lines m and n are parallel? A. ∠2!∠7 B. ∠1!∠4 C. ∠3 and ∠5 are complementary D. ∠6and∠8are supplementary
5. For what value of x is l⫽m in this figure?
6. If a⫽b, what is the value of x?
7. What value of x makes ΔDEF ! ΔJLK?
8. List the sides of ΔBCD in order from shortest to longest.
9. What is m∠C in quadrilateral ABCD?
10. Which point lies on the bisector of ∠PQR?
11. What is m∠TQM?
12. Which term best identifies !AB ? Why?
13. Three survey markers are located on a map at points H, I, and J. A triangle is formed by connecting these markers by string so that HI =150 feet, HJ = 245 feet, and IJ = 365 feet. Which statement is true about the measures of the angles of ΔHIJ? A. m∠H is the smallest B. m∠H is the largest C. m∠I is the smallest D. m∠I is the largest 14. Let p=Two angles are adjacent. Let q=They share a common side. Write the conditional statement p→q. Then write the symbolic and English form of the inverse, converse, contrapositive, and biconditional. 15. Provide a counterexample for the following statement: If an animal has four legs, then it is a dog. 16. Identify the hypothesis and conclusion of the conditional: If a triangle is a right triangle, then its two acute angles are complementary. What is the converse of the conditional statement? 17. B is between A and C. If AB=3x+2, BC=5x-‐10, and AC=16, what is the value of x? 18. What property justifies the following statement? If 4x+6=20, then 4x=14. 19. What is the measure of an interior angle of a regular decagon? 20. What are the values of x, y, and z?
21. What is the value of m?
22. What is m∠ABC?
23. What can you conclude about
!AB ?
24. Given the kite in the diagram, what are the values of x and y?
25-‐27: What is the most precise name for quadrilateral ABCD? 25.
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28-‐30: By what method can the triangles be proven congruent? Write a congruent statement for the triangles. 28.
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31. Reorder the reasons of the following proof to match the correct statements.
32. What must be true about the diagonals of a quadrilateral to prove that it is a rhombus? 33. What are the values of x and y?
34. Determine a value of x for which the figure is a rectangle. What must be true about the diagonals of a rectangle? Show that your value of x proves that the figure is a rectangle.
35. What is the image of (5,-‐1) under the translation (x,y) →(x-‐2,y+4)? 36. P’(4,-‐3) is the image of P under the translation (x,y) →(x+3,y-‐5). What are the coordinates of the pre-‐image point P?
37. What is the image of (-‐2,-‐5) reflected across x=2? 38. What is the measure of each exterior angle of a regular dodecagon? What are the coordinates of the vertices of the image ABCD for each transformation? 39. translation (x,y) →(x+4,y-‐2) 40. reflection across x=-‐1 41. rotation of 180° about the point (0,0)
42. What is the image of (2,-‐3) rotated 270° about the origin? 43. The perimeter of parallelogram JKLM is 72 in. If JK is 8 in. less than JM, what are the lengths of all four sides? 44. ABCD is a rhombus. m∠ABC=110. What are m∠BCA and m∠BAC? 45. The vertex angle of an isosceles triangle is three times the measure of a base angle. What is the measure of the vertex angle? 46. Two sides of a triangle are 4 cm and 9 cm. What are possible lengths for the third side? 47. Can a triangle be formed with side lengths that are 4, 9, and 12? Explain. 48. If the perimeter of isosceles triangle XYZ is 40 and XZ=16, what are the possible values for YZ? 49. Give the diagram at the right, which of the following must be true?
I. e+f=b+c II. f+c=a+d III. e+a+c=f+b+d
A. I only B. I and III C. I and II D. I, II, and III
50. ΔABC is an acute triangle. !BD⊥ AC and !BD bisects ∠ABC. m∠CBD=2x, and m∠ABD=4x-‐30. Draw a figure and find the measure of exterior angle BCF.
51. If ΔABC is similar to ΔADE, then AB: AD = ?: AE.
52. Is !AB a midsegment? Explain.
53. What is the perimeter of ΔABE?
54. What is the value of x?
55. What is the value of x?
56. Are the figures similar? If so, write a similarity statement.
57. Two figures have a similarity ratio of 2:5. The area of the smaller figure is 24 m2. What is the area of the larger figure? 58. ΔABC has vertices A(-‐1,3), B(0,7), and C(4,2). Find the image of ΔABC for a dilation with center (0,0) and a scale factor of 2. 59. A photographic negative is 2 in. by 1.5 in. An enlarged print from this negative has a length of 9 in. as its shorter side. What is the length of its longer side? 60. The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 10 and 12. What is the length of the altitude?