GEOMETRY
JUNE 2003 FINAL EXAMINATION
Part I:
1. Find the slope of the line which passes through the two points (10,-1) and (-3,9)
8
8
10
10
(1)
(2) 
(3)
(4) 
7
13
7
13
2. Find, in radical form, the distance between the points whose coordinates are (2,-4) and
(3,6)
(1)
(2) 3 11
(3)
(4) 21
101
6
3. What is the converse of the statement ~d → c?
(1) d → ~c
(2) c → ~d
(3) ~c → ~d
(4) ~d → ~c
4. Two angles are complementary, and in the ratio 1:5. Find the measure of the smaller
angle.
(1) 12
(2) 15
(3) 18
(4) 20
5. Which statement is logically equivalent to the statement: “If it is a tiger, then it has
stripes”?
(1) If it has stripes, then it is a tiger.
(2) If it is not a tiger, then it does not have stripes.
(3) If it does not have stripes, then it is not a tiger.
(4) If it is not a tiger, then it has stripes.
6. In the accompanying diagram, AB // CD and transversal EF intersects AB at point X and
CD at point Y. If m<XYD = 38, then find m<AXE.
E
A
X
B
(1) 38
(3) 102
C
Y 38˚
D
(2) 142
(4) 76
F
7. In the accompanying diagram of triangle ABC, DE // BC . If AD = 8, DB = 2 and
AE = 12, find EC.
A
8
(1) 3
(3) 6
(2) 4
(4) 10
D
12
E
2
B
C
8. Two triangles are similar. The lengths of the sides of the smaller triangle are 4, 6, and 8.
The shortest side of the larger triangle is 16. Find the length of the longest side of the
larger triangle.
(1) 24
(2) 40
(3) 32
(4) 48
9. Two opposite angles of a parallelogram measure 8x – 40 and 4x + 12. What is the
value of x?
(1) 7
(2) 5.2
(3) -13
(4) 13
10. Given ∆XYZ with XY  XZ . If m<Z = 62˚, find the m<X.
(1) 104˚
(2) 79˚
(3) 56˚
(4) 62˚
11. Find the value of x:
(1) 37˚
(3) 121˚
(2) 84˚
(4) 155˚
B
59˚
x
96˚
A
C
D
12. If the length of one base of a trapezoid is 24 and the length of the other base is 66, the
length of the midsegment of the trapezoid is:
(1) 90
(2) 50
(3) 45
(4) 40
13. Given the equation of the straight line 7x + 10y = 15, determine the slope of a line that
is parallel to the given line.
7
7
3
10
(1) 
(2)
(3)
(4)
2
10
10
7
14. The equation of a circle is (x – 5)2 + (y + 7)2 = 25. Find the center and the radius.
(1) center (5,-7), radius = 5
(3) center (-5,7), radius = 25
(2) center (5,7), radius = 25
(4) center (-5,-7), radius = 5
15. In the diagram, BD is a median to side AC in triangle ABC, and <1  <2.
Which method could be used to prove ∆ABD  ∆CBD?
B
(1) HL  HL
(3) SAS  SAS
(2) ASA  ASA
(4) AAS  AAS
1 2
A
D
16. The sum of the measures of the interior angles of a hexagon is:
(1) 1080˚
(2) 720˚
(3) 900˚
C
(4) 360˚
17. Find the coordinates of P', the image of P(-3,11) after a reflection in the x-axis.
(1) (-11,3)
(2) (-3,-11)
(3) (3,-11)
(4) (11,-3)
18. In right ∆ABC, CD is the altitude to hypotenuse AB . If CD = 12 and AD = 8, find DB.
(1) 4
(2) 10
(3) 18
(4) 20
19. If the lengths of two sides of a triangle are 8 and 15, which is a possible length of
the third side?
(1) 17
(2) 2
(3) 5
(4) 30
20. The letter H has:
(1) point symmetry only
(2) vertical line symmetry only
(3) horizontal line symmetry only
(4) all of the above
21. Straight line PQ is perpendicular to straight line RS . If the slope of PQ is
then the slope of RS is:
3
3
(1)
(2) 
4
4
(3)
4
3
(4) 
3
,
4
4
3
22. In the diagram, a triangle formed by joining the midpoints of a larger triangle has sides
whose lengths are 9, 11, and 14. What is the perimeter of the larger triangle?
B
(1) 34
(3) 68
(2) 17
(4) 136
D
11
A
E
9
14
F
C
23. If the length of a rectangle is 8 and the width is 2, find the diagonal of the rectangle.
(1) 2 15
(2) 3 6
(3) 2 17
(4) 10
24. Given ∆DEF with m<D = 40 and m<E = 30, which of the following statements is true?
(1) DF  EF
(3) EF is the shortest side
(2) DE is the shortest side
(4) DF is the shortest side
25. Which set of integers represents a Pythagorean triple:
(1) {2,3,4}
(2) {5,12,13}
(3) {8,9,10}
(4) {6,7,8}
26. In circle O, AB and AC are chords. If mAB = 80 and mAC = 70, find m<BAC.
A
70˚
(1) 40
(3) 105
80˚
O C
(2) 50
(4) 110
B
27. In right triangle ABC, find the measure of angle B, to the nearest degree.
A
(1) 33˚
(3) 50˚
7
(2) 40˚
(4) 32˚
C
11
B
28. All of the following are properties of an isosceles trapezoid except:
(1) Both pairs of opposite sides are congruent.
(2) The diagonals are congruent.
(3) The non-parallel sides are congruent.
(4) The base angles are congruent.
Part II:
1. In parallelogram ABCD, altitude AE is drawn to side DC . If AD = 8 feet, DC = 50 feet
and m<D = 30, find, in square feet, the area of parallelogram ABCD.
A
B
8 ft
30˚
D
E
C
50 ft
2. If the circumference of a circle is 8  inches, what is the area, in square inches, of the circle?
(Leave the answer in terms of  )
3. In the diagram, ABCD is a square, and triangle DEC is contained in the square so that
side DC of the square is the same as base DC of triangle DEC. If DC = 10 meters,
find, in square meters, the area of the shaded portion of the diagram.
A
E
D
B
C
10 meters
4. In the diagram, AB and CD are straight lines which intersect at E. If m<AEC = 3x – 50
and m<DEB = x + 20, find m<AEC.
A
D
E
3x – 50
x + 20
C
B
5. In the diagram, ABC is a straight line and ray BD is drawn. If m<DBA = 8x – 40 and
m<DBC = 2x – 10, find m<DBA.
D
A
8x – 40 2x – 10
B
C
Part III:
1. You are given the measure of one side and one angle of a right triangle. Angle S
is a right angle, ST = 13, and m<T = 34. Find the lengths of the other two sides
and the measure of the other acute angle. Round your answers to two decimal places.
You must show/explain work for credit. Make sure all of your answers are clearly labeled.
R
S
Find: 1) m<R
2) RS
13
34˚
3) RT
T
2. Given: Triangle PQR with vertices P(8,6), Q(-6,8), and R(-4,-8)
a) Graph and label ∆PQR
b) Find the coordinates of S, the midpoint of QR and T, the midpoint of PR
1
c) Show that ST = QP
2
d) Show that ST // QP
3. Given: Triangle XYZ with coordinates X(-6,2), Y(-2,1), and Z(-4,6)
a) Graph and label ∆XYZ
b) Graph and state the coordinates of ∆X'Y'Z', the image of ∆XYZ after
a reflection in the y-axis.
c) Graph and state the coordinates of ∆X''Y''Z'', the image of ∆XYZ after
a translation, T5,-4.
d) Graph and state the coordinates of ∆X'''Y'''Z''', the image of ∆XYZ after
a dilation, D2.
4. In the accompanying diagram of circle O, tangent PA , secant PGFB , diameter AOEB ,
and chord CEFD are drawn; mCA = 70, mDG = 90, and m<CEA = 40.
C
Find:
A
a) mCB
b) mBD
c) m<APB
E O
d) m<PAB
e) m<ABG
B
F
G
P
D
Part IV:
1. In right triangle ABC, CD is the altitude drawn to hypotenuse AB . The length
of AD is 21 inches less than the length of BD.
a) If BD = x, write an expression for the length of AD, in terms of x.
b) If CD = 10, find the length of AD.
C
A
D
B
2. Given: Triangle ABC with vertices A(-5,8), B(7,4), and C(3,-6):
a) Graph and label triangle ABC.
b) Find the area of triangle ABC.
3. Write a valid two-column proof.
Given: BD  AC
D is the midpoint of AC
B
Prove: AB  CB
A
1 2
D
C
NAME_________________________________________
MRS. BINASO
GEOMETRY
EASTER ASSIGNMENT
JUNE 2003 FINAL EXAMINATION
This assignment is DUE ON 4/16.
Part I: Place the number of the correct choice on the line provided. Show all work on loose
leaf and attach to this answer sheet.
1. ______
8. ______
15. ______
22. ______
2. ______
9. ______
16. ______
23. ______
3. ______
10. ______
17. ______
24. ______
4. ______
11.______
18.______
25.______
5. ______
12.______
19.______
26.______
6. ______
13.______
20.______
27.______
7. ______
14.______
21.______
28.______
Part II: Show all work in the space provided.
1.
2.
3.
4.
5.
Part III: Show all work. Attach your graph paper to the answer sheet for numbers 2 and 3.
1.
4.
Part IV: Show all work. Attach your graph paper to the answer sheet for number 2.
1.
3.