geo sem 1 final review winter break good - weebly
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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 = ________
Ð
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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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