Download GeoH Quarterly # 3 Review Packet

6325 - 1 - Page 1
Name: ____________________________________________
1)
3)
Given: AC C AD
A1 C A2
M is the midpoint of DC
Given: PQ = DE
PB = AE
QA B PE
DB B PE
Prove: CB C DA
Prove: AD C AQ
4)
2)
Given: CA = CB
CR = CS
DR B AC
DS B CD
Prove: DR = DS
Given: TR C TS
MR C NS
Prove: RN C MS
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5)
7)
Given: CD C CE
AE B BC
BD B AC
Given: AB C ED
FE C CB
FE B AD
CB B AD
Prove: AE C BD
Prove: hAEF C hCBD
6)
8)
What is the converse of the statement "If it is
Sunday, then I do not go to school"?
A) If it is not Sunday, then I do not go to school.
B) If I do not go to school, then it is Sunday.
C) If I go to school, then it is not Sunday.
D) If it is not Sunday, then I go to school.
9)
What is the inverse of the statement "If Mike did his
homework, then he will pass this test"?
A) If Mike passes this test, then he did his
homework.
B) If Mike does not pass this test, then he only
did half his homework.
C) If Mike does not pass this test, then he did not
do his homework.
D) If Mike did not do his homework, then he will
not pass this test.
Given: PQ C PR
QB B PR
RA B PQ
Prove: AR C QB
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10)
Which is logically equivalent to the statement "If I
live in New York, then I live in the United States"?
A) If I live in the United States, then I live in New
York.
B) If I do not live in the United States, then I do
not live in New York.
C) If I do not live in New York, then I do not live
in the United States.
D) If I do not live in the United States, then I live
in New York.
11)
In hPQR, PQ = 5, QR = 14 and PR = 11. What is
the smallest angle?
A) AR
B) AP
15)
What is the value of x?
A) 40
B) 8
C) AQ
12)
Which set of numbers can not represent the lengths
of the sides of a triangle?
A) {3,4,5}
C) {2,3,4}
B) {1, 3,2}
D) {1,1,2}
13)
What is the value of x that makes l1 H l2?
In the accompanying diagram of
parallelogram ABCD, diagonals AC and DB
intersect at E, AE = 3x - 4, and EC = x + 12.
16)
What is the length of a side of a square whose
diagonal measures 4 2?
17)
In rectangle ABCD with diagonals AC and BD,
AC = 3x - 15 and BD = 7x - 55. Find x.
18)
The diagonals of a rhombus are 6 and 4. What is
the measure of each side?
A) 5
B) 4
A) 10
B) 20
14)
C) 6
D) 12
C) 16
D) 20
19)
C)
D)
In the diagram below, PQRS is a rhombus with
diagonals PR and SQ.
What is the value of x that makes l1 H l2?
If mASRQ = 50D, find mARSQ.
A) 11.6
B) 26.6
C) 10
D) 8
13
52
20)
Which statement about a figure ABCD would
always be true?
24)
A) If ABCD is a parallelogram, then it must be a
trapezoid.
B) If ABCD is a rectangle, then it must be a
square.
C) If ABCD is a quadrilateral, then it must be a
parallelogram.
D) If ABCD is a parallelogram, then it must be a
quadrilateral.
21)
Which statement is not always true about a
parallelogram?
A) Opposite angles are congruent.
B) Opposite sides are congruent.
C) Opposite sides are parallel.
D) Diagonals are congruent.
22)
Which quadrilateral must have congruent diagonals?
A) parallelogram
C) rectangle
B) trapezoid
D) rhombus
23)
In the accompanying diagram of isosceles
trapezoid ABCD, AB H DC and diagonals DB and
AC intersect at E.
6325 - 1 - Page 4
In the diagram below, PQRS is a trapezoid with
SR H PQ. TU is the median.
If SR = 2x - 3, PQ = 2x + 11, and TU = 14, what
is the length of PQ?
A) 5
C) 21
B) 29
D) 7
25)
If point P lies on line l, which diagram represents
the locus of points 3 centimeters from point P?
A)
B)
C)
Which statement is not true?
A)
B)
C)
D)
AC C BD
hADC C hABC
ACDB C ADBA
hCBA C hDAB
D)
26)
Parallel lines l and m are 4 units apart and P is a
point on line m. How many points are equidistant
from l and m and 2 units from P?
A) 1
B) 2
C) 3
D) 0
6325 - 1 - Page 5
27)
P is a point on line l. How many points are 3 units
from l and 4 units from P?
A) 1
B) 2
28)
29)
30)
32)
C) 0
D) 4
What equation describes the locus of points
equidistant from A(-3,2) and B(-3,8)?
A) x = -3
C) y = -3
B) y = 5
D) x = 5
What is the equation of the locus of points passing
through point (3,-2) and 3 units from the y-axis?
A) x = -2
C) y = -2
B) y = 3
D) x = 3
(x
(x
(x
(x
- 2)2 + (y + 1)2 = 16
+ 2)2 + (y - 1)2 = 16
+ 2)2 + (y + 1)2 = 16
- 2)2 + (y - 1)2 = 16
In hQRS, mAQ = xD, mAR = (8x - 40)D, and
mAS = 2x D. Which type of triangle is hQRS?
C) (3,-13)
B) (-1,-5)
D) (9,11)
Segment AB has endpoints A(-1,3) and B(0,7).
What is the length of AB?
10
101
C)
D)
5
17
37)
Write an equation of the line that passes through the
points (-1,-2) and (5,1).
38)
Classify the graphs of y + x = 4 and y - x = 4 as
parallel, perpendicular, or neither.
39)
An equation of the circle whose center is (-3,1) and
whose radius is 8 is
C) 1,800D
D) 540D
What is the number of sides of a regular polygon if
each interior angle measures 160D?
A) 16
B) 18
A)
B)
C)
D)
40)
C) isosceles
D) obtuse
What is the sum of the measures of the interior
angles of a octagon?
A) 1,080D
B) 1,440D
34)
A) (4 ,5 )
A)
B)
How many total number of points are 5 units from
the point (4,-2) and 2 units from the x-axis?
A) 5
C) 3
B) 2
D) 4
A) acute
B) right
33)
36)
If M(4,-8) is the midpoint of AB and the
coordinates of A are (5,-3), what are the
coordinates of B?
An equation of the locus of points 4 units from the
point (2,-1) is
A)
B)
C)
D)
31)
35)
C) 17
D) 15
(x
(x
(x
(x
+ 3)2 + (y - 1)2 = 8
+ 3)2 + (y - 1)2 = 64
- 3)2 + (y + 1)2 = 64
- 3)2 + (y + 1)2 = 8
The transformation R90D maps point (5,6) onto the
point whose coordinates are
A) (-6,5)
C) (6,-5)
B) (5,-6)
D) (6,5)
41)
Which transformation does not preserve
orientation?
A) rotation
B) translation
C) reflection in the y-axis
D) dilation
6325 - 1 - Page 6
42)
Find the mean proportional (geometric mean)
between 4 and 5.
47)
In hABC, a = 4, b = 3, and cos C = * . What is
the length of c?
A) 13
B) 7
43)
44)
The areas of two similar triangles are 25 sq cm and
9 sq cm. If the length of a side of the larger triangle
is 20 cm, find the length of the corresponding side
of the smaller triangle.
48)
C)
D)
19
37
In the accompanying diagram of hABC,
mAA = 30D, mAC = 50D, and AC = 13.
Use the information marked on the figure to find the
value of x.
What is the length of side AB to the nearest tenth?
A) 6.6
C) 11.5
B) 10.1
D) 12.0
49)
45)
46)
In a right triangle, the 3 sides are 10, 24, and 26.
Find the value of all six trigonometric functions of
the smaller acute angle.
In hABC, mAB = 60D, a = 6, and c = 10. What is
the area of hABC?
A) 15 3
B) 30 3
50)
C) 30
D) 15
In hPQR below, S and T are midpoints of PQ and
QR, respectively.
In an accompanying diagram of a right
triangle ABC, the length of BC is 70 feet and the
measure of the angle b is 20D. Find, to the nearest
foot, the length of AC.
If ST = 12 and PR = 2x + 4, what is the value of x?
A) 10
C) 8
B) 4
D) 14
51)
If a triangle has sides of 6, 8, and 12, what is the
perimeter of the triangle formed by connecting the
midpoints of the sides of the original triangle?
6325 - 1 - Page 7
52)
In the accompanying diagram, DE H BC, AD = 8,
AB = 12, and EC = 5.
54)
In the diagram below of right hRST, TP is the
altitude to hypotenuse RS.
If TP = 6 and RP is 5 less than PS, find the length
of hypotenuse RS.
Find AE.
55)
53)
Solve for x:
In hABC, find x given that DE H AB.
56)
Given: PQ C PS
PR bisects AQPS
Prove: hPQR ~ hPRS