Name: ___________________________ Date: _____________ Block: ______

Geometry Semester 1 Final Review for Winter Break

CHAPTER 1 1. Draw and label each of the following.

a) a line containing points R and S. b) a ray with endpoint B that passes through L. c) a plane containing a segment with endpoints X and Y.

2. Use the diagram at right to name each of the following.

a) three collinear points b) a plane containing T, X, and Y. c) two segments d) a line containing Q and T.

3. Use the diagram at right to find the length of each segment.

a)

b)

4. T is between R and V. RV = 31 and VT = 14. Find RT. 5. Use the diagram at right to find AB.

MP

NQ

YOUMUSTSHOWALLYOURWORKTOGETANYCREDIT!

6. M is the midpoint of . AM = 11x – 9 and BM = 7x + 35. a) Find the value of x. b) Find AM. c) Find BM.

7. Name all of the angles in the diagram at right. 8. Classify each angle measure by its measure.

a) m XYZ = 90° b) m PQR = 17° c) m BRZ = 178°

_______________ _______________ _______________

9. bisects LMP, m LMT = (4x – 13)°, and m TMP = (2x + 17)°. Find mLMP.

10. Use the diagram at right to determine whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

a) 2 and 3 b) 1 and 5 c) 3 and 1

11. Find the perimeter and area of each figure.

a) b)

perimeter: ____________ perimeter: ____________

area: ________________ area: ________________

AB

∠ ∠ ∠

MTu ruu

∠ ∠ ∠ ∠

∠ ∠

∠ ∠

∠ ∠

c) d)

perimeter: ____________ perimeter: ____________

area: ________________ area: ________________

12. Find the coordinates of the midpoint of with endpoints H(-7, -4), and J(3, -2).

13. S is the midpoint of , R has coordinates (-5, 1) and the midpoint S has coordinates of (-1, 4). Find the coordinates of T . 14. Use the diagram at right to find LM and NP to the nearest tenth. Then determine if .

CHAPTER 2 15. Write a conditional statement, converse, inverse, and contrapositive for each of the

following. Then determine whether each statement is True or False. a) The midpoint M of a segment bisects the segment.

conditional statement: _____________________________________________

_____________________________________________________ True / False

converse: _______________________________________________________

_____________________________________________________ True / False

inverse: _________________________________________________________

_____________________________________________________ True / False

contrapositive: ____________________________________________________

_____________________________________________________ True / False

HJ

RT

LM ≅ NP

b) conditional statement: ________________________

___________________________________________

________________________________ True / False

converse: __________________________________

_____________________________________________________ True / False

inverse: _________________________________________________________

_____________________________________________________ True / False

contrapositive: ____________________________________________________

_____________________________________________________ True / False

CHAPTER 3 17. Use the diagram at right to give an example of each angle pair.

a) same-side interior angles b) alternate exterior angles c) corresponding angles d) linear pair e) alternate interior angles f) vertical angles

18. Use the diagram at right to find the value of x. List the postulate or

theorem used. 19. For each diagram, find the value of x. Then find each angle measure.

a) b)

wings

butterfly

20. Write the equation of the line through (-3, -1) and (3, -3) in slope-intercept form.

21. Write the equation of the line through (6, -2) with slope in point-slope form.

22. Write the equation of the line with y-intercept -3 through the point (2, 5) in point- slope form. 23. Write the equation of the line with x-intercept -4 and y-intercept 2 in slope-intercept form.

24. Graph each pair of lines and use their slopes to determine if they are parallel, perpendicular, coincident, or neither.

a) and for A(-1, 0), B(1, 5), C(4, 5), D(-2, 4)

b) and for L(-3, 2), M(-1, 5), N(2, 3), P(1, -5)

_______________ _______________

−

34

ABs ruu

CDs ruu

LMs ruu

NPs ruu

c) and for P(2, -1), Q(0, 0), R(-4, 2), S(-2, 1)

d) and for F(-3, 2), G(-2, 5), H(2, 4), J(2, 1)

_______________ _______________

25. Graph each line.

a) y = 3x – 1 b) c) y = -5 d) x = 3

26. Write the equation of each line.

a)

b)

______________ ______________

CHAPTER 4 28. Use the diagram at right to classify each triangle by its angle measures.

a) ΔQPR: ________________________ b) ΔSRQ: ________________________ c) ΔTRQ: _________________________

PRs ruu

QSs ruu

GHs ruu

FJs ru

y −1=

35

(x + 2)

29. Use the diagram at right to classify each triangle by its side lengths.

a) ΔQNM: ________________________ b) ΔMPQ: ________________________ c) ΔNLM: _________________________

30. For each diagram, find the specified angle measure.

a) m GFC b) m BAC

31. Find each measure.

a) DC b) BC c) LM

____________ ____________ ____________

32. Determine whether the side lengths can form a triangle. a) 3, 4, 5 b) 7, 9, 16 c) 2000, 2000, 1

_______ _______ _______ CHAPTER 5 33. Write the equation of the perpendicular bisector for each segment.

a) with A(-7, 10) and B(-5, 4) b) with R(4, 3) and S(-6, -1)

∠ ∠

AB RS

34. Sketch the three perpendicular bisectors for the triangle. Label the circumcenter C and sketch the circumcircle. 35. Sketch the three angle bisectors for the triangle. Label the incenter I and sketch the incircle.

36. and are angle bisectors of ΔABC. a) Find m BCP.

b) Find the distance from P to . 37. Sketch the three medians for the triangle below. Label the centroid C. 38. Sketch the three altitudes for the triangle below. Label the orthocenter O. 39. Use the diagram at right to find the following measurements.

a) EF b) AB c) m EDF

PC PB

∠

BC

∠

y m

40. Use the diagram at right to complete the statements below.

is a _______________ of ΔJKL because it is a

segment that joins the _______________ of two sides

of the triangle. XY = ½( ______ ) and is

_______________ to .

41. For each triangle, write the interior angles in order from smallest to greatest. a) b)

42. For each triangle, write the side lengths in order from shortest to longest. a) b)

43. For each triangle, find the missing side length(s). Write in reduced radical form.

a) b) c)

XY

XY

JL

44. A park developer wants to put a bike trail from one corner of a rectangular park to the opposite corner. What will be the length of the trail? Round to the nearest yard. 45. Use the given triangle side lengths to classify the triangle as acute, right, obtuse, or

impossible. a) 10, 24, 26 b) 4, 5, 7 c) 20, 22, 24

______________ ______________ _______________ CHAPTER 8 46. Using the figure at right, write each trigonometric

ratio as a simplified fraction and as a decimal rounded to the nearest hundredth. a) sin A b) cos B c) tan B

______ ______ ______ ______ ______ ______

47. Find each length. Round to the nearest hundredth. a) b) c)

XZ = ________ HI = ________ KM = ________

48. Solve the triangles by finding all unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. a) b)

KL = __________ EF = __________

JK = __________ m D = ________

m K = ________ m F = ________

49. Maria is snorkeling and sees a turtle on the ocean floor at an angle of depression of 38°. She is 14 feet above the ocean floor. How far from the turtle is she? Round your answer to the nearest foot.

50. Find the measure of the angle formed between the line y = 5x and the x-axis.

51. Find each measure. Round lengths to the nearest tenth and angle measures to the

nearest degree. a) b)

BC = ________ m J = ________

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Ð Ð

Ð

c) d)

YZ = ________ m I = ________

52. Find the area of each triangle.

a) b)

Area = __________ Area = __________

c) d)

Area = __________ Area = __________

CHAPTER 7 53. Solve each proportion.

a) b)

c) d)

Ð

x +132

=8

x +1 2(h − 4)

6=

h9

26 20

15 11

7

9 8

48°

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28 54

54. Solve for the missing lengths in the sets of similar figures below. a)

b)

55. Determine whether the triangles are similar. Fully explain why. .

a)

b)

c)

N

U V

L

M

T 7

5

3.5

24.5

17.5

12

7

11 27.5

x

6 1.5

9

a