Geometry – Fall 2009
Final Exam Part II
Name __________________________
Date___________________Period___
1
Formulas:
x2  x1 2   y2  y1 2
Distance:
 x  x 2 y1  y 2 
Midpoint:  1
,

2 
 2
y  y1
Slope: 2
x2  x1
Circles: Area = r 2 Circumference = 2r
Slope Intercept Form: y  mx  b
Point Slope Form: y  y1  mx  x1 
Write the letter that represents the correct solution on the line provided.
Chapter 1:
_____ 1. Find the length of segment AB with endpoints A(5, -1) and B(1, 2).
A. 4
B. 5
C. 7
D. 3 5
_____ 2. Find the midpoint of segment XY with endpoints X(-3, -1) and Y(5, -7).
A. (-4, 3)
B. (1, -4)
C. (-1, 4)
D. (2, -8)
_____ 3. Find the perimeter and the area of the figure.
A. P = 19 cm, A = 78 cm²
B. P = 24 cm, A = 28 cm²
C. P = 31 cm, A = 50 cm²
D. P = 38 cm, A = 78 cm²
_____ 4. Find the circumference of the circle. Leave your answers in terms of π.
A. 121 
B. 11 
C. 22 
D. 484 
_____ 5. Find the area of the circle. Leave your answers in terms of π.
A. 4 
B. 8 
C. 16 
D. 64 
Chapter 2:
_____ 6. What conclusion can you draw from the two given statements?
If three points lie on the same line, then they are collinear.
If three points are collinear, then they line in the same plane.
A.
B.
C.
D.
If three points do not lie in the same plane, then they do not lie on the same line.
The three points are collinear.
The three points lie in the same plane.
If three points lie on the same line, then they lie in the same plane.
_____ 7. Which statement provides a counterexample to the following faulty definition?
A square is a figure with four congruent sides.
A.
B.
C.
D.
A six-sided figure can have four sides congruent.
Some triangles have all sides congruent.
A square has four congruent angles.
A rectangle has four sides.
_____ 8. Use the diagram at the right to find the measure of
A. 26°
B. 38°
C. 52°
D. 90°
_____ 9. Use the diagram at the right to find the measure of
A. 64°
B. 76°
.
C. 128°
.
D. 90°
_____ 10. Find the value of x in the figure at the right.
A. 13
B. 50
C. 51.5
D. 87
_____ 11. Find the value of x in the figure at the right.
A. 4
B. 9
C. 10
D. 12
12. Complete the two-column proof.
Given: C is the midpoint of FH.
Prove: x = 6
Statements
Reasons___________
1. C is the midpoint of FH.
a. __________________________________
2. FC = CH
b. __________________________________
3. 4x = 2x + 12
c. __________________________________
4. 2x = 12
d. __________________________________
5. x = 6
e. __________________________________
Chapter 3:
_____ 13. Find the value of x for which l // m.
A. x = 35
B. x = 26
C. x = 10
D. x = 40
_____________
_____ 14. Find the values of x and y.
A. x = 22, y = 120
B. x = 38, y = 104
C. x = 60, y = 102
D. x = 120, y = 22
_____ 15. Find the values of x, y, and z.
A. x = 45, y = 35, z = 45
B. x = 55, y = 125, z = 35
C. x = 35, y = 35, z = 55
D. x = 55, y = 55, z = 55
_____ 16. Find the values of x and y.
A. x = 91, y = 108
B. x = 90, y = 109
C. x = 94, y = 105
D. x = 94, y = 81
_____ 17. Find the value of the missing angle measure.
A. x = 53
B. x = 307
C. x = 100
D. x = 127
_____ 18. Write an equation, in point-slope form, of the line that is perpendicular to y = 2x + 17
and contains (8, -1).
1
A. y  1   ( x  8)
2
B. y  1  2( x  8)
C. y  8  
1
x  1
2
D. y  1 
1
( x  8)
2
_____ 19. Write the equation of the line that passes through the points (6, 4) and (-3, 1).
A. y  3 x  14
B. y  3 x  10
C. y 
1
x6
3
D. y 
_____ 20. Determine whether the lines are parallel, perpendicular, or neither.
A. Parallel
B. Perpendicular
C. Neither
1
x2
3
2x  3y  6
4 x  6 y  24
Chapter 4:
_____ 21. State the postulate or theorem you would use to prove the pair
of triangles congruent. If the triangles cannot be proved
congruent, write not possible.
A. SAS
B. ASA
C. AAS
D. Not Possible
_____ 22. State the postulate or theorem you would use to prove the pair
of triangles congruent. If the triangles cannot be proved
congruent, write not possible.
A. SSS
B. ASA
C. AAS
D. Not Possible
_____ 23. What other information do you need in order to prove the triangles
congruent using the SAS Congruence Postulate?
A. CBA  CDA
_____
B. BAC  DAC
_____
_____
_____
D. BC  DC
C. AB  AD
_____ 24. If ΔMNO  ΔPQR, which of the following can you NOT conclude as being true?
_____
_____
A. MN  PR
B. M  P
_____
_____
C. NO  QR
D. N  Q
25. Complete the two-column proof.
Given: AB // DC,  B   D
Prove: BC  DA
Statements
_____
Reasons_________________
_____________
_____
1. AB // DC
a. ________________________________________
2.  BAC   DCA
b. ________________________________________
3.  B   D
c. ________________________________________
4. AC  AC
d. ________________________________________
5. ΔABC  ΔCDA
e. ________________________________________
6. BC  DA
f. ________________________________________
_____ 26. Find the value of y in the isosceles triangle.
A. 50
B. 65
C. 80
D. 130
Chapter 5:
_____ 27.
is the midsegment of
A. 18
B. 36
. NO = 36, find MP.
C. 54
D. 72
C. 7
D. 2
C. 9
D. 18
_____ 28. Find the value of x.
A. 8
B. 1
_____ 29. Find the value of y.
A. 16.2
B. 27
_____ 30. List the sides of the triangle in order from shortest to longest.
A. BC, CA, AB
B. AB, CA, BC
C. CA, BC, AB
D. BC, AB, CA
_____ 31. If a triangle has side lengths 18ft and 20ft, what are the possible lengths of the third side?
A. 2 < x < 38
B. 18 < x < 20
C. 2 < x < 20
_____ 32. Which line contains an altitude of ΔABC?
A. l
B. k
C. n
D. m
_____ 33. In ΔTUV, Y is the centroid. If YW = 5, find TY and TW.
A. TY = 5, TW = 10
B. TY = 7.5, TW = 12.5
C. TY = 10, TW = 15
D. TY = 2.5, TW = 7.5
Chapter 6:
_____ 34. Find the measure of  1 and  2.
A.
 1 = 28°,  2 = 28°
C.  1 = 28°,  2 = 56°
B.  1 = 56°,  2 = 28°
D.  1 = 56°,  2 = 56°
D. 2 < x < 18
_____ 35. FCHS is a rectangle. If FH = 9x – 14 and CS = 7x + 4, find the value of x and
the length of each diagonal.
A. x = 9; FH = 95; CS = 95
B. x = 6; FH = 46; CS = 46
C. x = 9; FH = 67; CS = 67
D. x = 6; FH = 40; CS = 46
_____ 36. Find the measure of  1 and  2.
A.  1 = 75°,  2 = 105°
B.  1 = 105°,  2 = 75°
C.  1 = 75°,  2 = 75°
D.  1 = 105°,  2 = 105°
_____ 37. Find the side lengths of the kite.
A. 9, 9, 13, 13
B. 11, 11, 20, 20
C. 9, 9, 11, 13
D. 11, 13, 20, 20
_____ 38. Find the measure of  1 and  2.
A.  1 = 90°,  2 = 40°
B.  1 = 40°,  2 = 90°
C.  1 = 40°,  2 = 50°
D.  1 = 50°,  2 = 90°
_____ 39. Find the value of x and y.
A. x = 33, y = 81
B. x = 99, y = 81
C. x = 33, y = 147
D. x = 40, y = 140
_____ 40. Which statement is true for some, but not all, rectangles?
A.
B.
C.
D.
Opposite sides are parallel.
It is a parallelogram.
Adjacent sides are perpendicular.
All sides are congruent.