Download Regents Geometry Ch. 6 Review

Regents Geometry Ch. 6 Review
Name:
1.
2.
3.
Date:
The sum of the interior angles of a polygon of n
sides is
A.
360
C.
(n
B.
2) 180
D.
4.
In the diagram below, MATH is a rhombus with
diagonals AH and MT.
360
n
(n
2) 180
n
The measure of an interior angle of a regular
polygon is 120 . How many sides does the
polygon have?
If mOHAM = 12, what is mOAMT?
A.
A.
5
B.
6
C.
3
D. 4
The number of degrees in the sum of the interior
angles of a pentagon is
A.
72
B.
360
C.
540
5.
D. 720
page 1
12
B.
78
C.
84
D. 156
Find, in degrees, the measures of both an interior
angle and an exterior angle of a regular pentagon.
6.
In the diagram below of rhombus ABCD,
mOC = 100.
10.
11.
What is mODBC?
A.
7.
45
C.
50
D. 80
75
B.
80
C.
105
12.
D. 180
Melissa is walking around the outside of a
building that is in the shape of a regular polygon.
She determines that the measure of one exterior
angle of the building is 60 . How many sides
does the building have?
A.
9.
B.
The measures of ve of the interior angles of
a hexagon are 150 , 100 , 80 , 165 , and 150 .
What is the measure of the sixth interior angle?
A.
8.
40
6
B.
9
C.
3
If each interior angle of a regular polygon
measures 135 , the polygon must be
A.
an octagon
B.
a decagon
C.
a hexagon
D. a pentagon
In the accompanying diagram, what is the total
number of distinct diagonals that can be drawn
from vertex A ?
A.
1
B.
2
C.
3
D. 4
Which reason could be used to prove that a
parallelogram is a rhombus?
A.
Diagonals are congruent.
B.
Opposite sides are parallel.
C.
Diagonals are perpendicular.
D. Opposite angles are congruent.
13.
D. 12
Which type of gure is shown in the accompanying
diagram?
If each interior angle of a regular polygon
measures 170 , what is the total number of sides
in the polygon?
A.
10
B.
17
C.
18
D. 36
page 2
A.
hexagon
B.
octagon
C.
pentagon
D. quadrilateral
Regents Geometry Ch. 6 Review
14.
In the accompanying diagram of rhombus ABCD,
mOCAB = 35. Find mOCDA.
15.
In rectangle ABCD, AC and BD are diagonals. If
mO1 = 55, nd mOABD.
16.
17.
As shown in the diagram below, the diagonals
of parallelogram QRST intersect at E. If
QE = x2 + 6x, SE = x + 14, and TE = 6x 1,
determine TE algebraically.
18.
In rhombus ABCD, the measure, in inches, of AB
is 3x + 2 and BC is x + 12. Find the number of
inches in the length of DC.
19.
In the accompanying diagram of parallelogram
ABCD, mOB = 5x and mOC = 2x + 12. Find the
number of degrees in OD.
20.
In the accompanying diagram of parallelogram
ABCD, diagonals AC and intersect BD at E,
BE = 2x and ED = x 10.
As shown in the diagram of rectangle ABCD
below, diagonals AC and BD intersect at E.
If AE = x + 24 and BD = 4x
of AC is
16, then the length
A.
12
6
B.
10
C.
What is the value of x?
D. 24
A.
page 3
30
B.
30
C.
6
D. 6
Regents Geometry Ch. 6 Review
21.
In rectangle ABCD, AC = 3x + 15 and BD = 4x
Find the length of AC.
5.
22.
In the accompanying diagram of
parallelogram ABCD, mOA = (2x + 10)
and mOB = 3x. Find the number of degrees in
mOB.
23.
In the accompanying diagram of rectangle ABCD,
mOBAC = 3x + 4 and mOACD = x + 28.
26.
In rhombus ABCD, AB = 2x
Find the length of BC.
2 and BC = x + 8.
27.
In the accompanying diagram, ABCD is a
parallelogram with mOB = 120, mOC = 60,
mOD = 2x + 5y, and mOA = 4x + y. Find the
values of x and y. Check your solution.
28.
If the length of the side of a rhombus is
represented by x + 3, which expression represents
the perimeter of the rhombus?
A.
4x + 3
B.
4x + 12
C.
x2 + 9
D. x2 + 6x + 9
What is mOCAD ?
A.
24.
B.
37
C.
40
D. 50
29.
The length of a side of a square is represented by
(3x 1). If the perimeter of the square is 68, nd
the value of x.
30.
Parallelogram ABCD has coordinates A(1; 5),
B(6; 3), C(3; 1), and D( 2; 1). What are the
coordinates of E, the intersection of diagonals AC
and BD?
If two consecutive sides of a rhombus are
represented by 3x 6 and x + 14, then the
perimeter of the rhombus is
A.
25.
12
10
B.
24
C.
72
D. 96
In rectangle DATE, diagonals DT and AE intersect
at S. If AE = 40 and ST = x + 5, nd the value
of x.
page 4
A.
(2; 2)
B.
(4:5; 1)
C.
(3:5; 2)
D. ( 1; 3)
Regents Geometry Ch. 6 Review
31.
35.
In rhombus ABCD, the diagonals AC and BD
intersect at E. If AE = 5 and BE = 12, what is the
length of AB?
A.
7
B.
10
C.
13
D. 17
Given three distinct quadrilaterals, a square, a
rectangle, and a rhombus, which quadrilaterals
must have perpendicular diagonals?
A.
the rhombus, only
B.
the rectangle and the square
C.
the rhombus and the square
D. the rectangle, the rhombus, and the square
32.
The length of one side of a square is 13 feet.
What is the length, to the nearest foot, of a
diagonal of the square?
A.
13
B.
18
C.
19
36.
D. 26
Which statement is true about every parallelogram?
A.
All four sides are congruent.
B.
The interior angles are all congruent.
C.
Two pairs of opposite sides are congruent.
D. The diagonals are perpendicular to each other.
33.
If the sides of a rectangle have lengths 7 and 12,
nd the length of a diagonal to the nearest tenth.
37.
34.
In parallelogram ABCD shown below, diagonals
AC and BD intersect at E.
Which statement is false?
A.
All parallelograms are quadrilaterals.
B.
All rectangles are parallelograms.
C.
All squares are rhombuses.
D. All rectangles are squares.
38.
Which statement must be true?
Which statement about quadrilaterals is true?
A.
All quadrilaterals have four right angles.
A.
AC = DB
B.
OABD = OCBD
B.
All quadrilaterals have equal sides.
C.
^ AED = ^CEB
D. ^DCE = ^BCE
C.
All quadrilaterals have four sides.
D. All quadrilaterals are parallelograms.
page 5
Regents Geometry Ch. 6 Review
39.
A quadrilateral must be a parallelogram if one pair
of opposite sides is
A.
congruent, only
B.
parallel, only
C.
congruent and parallel
43.
D. parallel and the other pair of opposite sides is
congruent
40.
are congruent
B.
bisect each other
C.
bisect the angles through which they pass
B.
AC = BD
C.
AC bisects ODAB and O BCD.
Which statements describe properties of the
diagonals of a rectangle?
I.
42.
AC ? BD
44. In the accompanying diagram of rhombus QRST,
diagonals QS and RT intersect at M. Which
statement must be true?
D. are perpendicular to each other
41.
A.
D. AC and BD bisect each other.
A parallelogram must be a rectangle if its
diagonals
A.
If quadrilateral ABCD is a parallelogram, which
statement must be true?
The diagonals are congruent.
A.
Triangle QRM is an isosceles right triangle.
II. The diagonals are perpendicular.
B.
^QRM = ^SRM
III. The diagonals bisect each other.
C.
Triangle QRM is an obtuse triangle.
A.
II and III, only
B.
C.
I and III, only
D. I,II, and III
D. QS = RT
I and II, only
45.
Which statement about a parallelogram is not
always true?
A.
Diagonals are perpendicular.
B.
Opposite sides are congruent.
C.
Opposite angles are congruent.
Which statement would never be used to prove
that a gure is a rhombus?
A.
The gure is a quadrilateral.
B.
The gure has a pair of equal adjacent sides.
C.
The gure is a parallelogram.
D. The gure is a rectangle.
D. Consecutive angles are supplementary.
page 6
Regents Geometry Ch. 6 Review
46.
Which statement is always true about a
parallelogram?
A.
Diagonals bisect the angles.
B.
Diagonals are perpendicular.
C.
Adjacent sides are congruent.
49.
In the accompanying diagram of rectangle ABCD,
mOABE = 30 and mOCFE = 144. Find mOBEF.
50.
In the accompanying diagram, BCD, ACE,
AB ? BCD, and CE = ED. If mOA = 50, nd the
measure of OE.
D. Diagonals bisect each other.
47.
Which statement is always true?
A.
Rhombuses are squares.
B.
Parallelograms are rectangles.
C.
Rectangles are squares.
D. Squares are rectangles.
48.
In the diagram below of parallelogram ABCD
with diagonals AC and BD, mmO 1 = 45 and
mODCB = 120 .
What is the measure of O2?
A.
15
B.
30
C.
45
D. 60
page 7
Regents Geometry Ch. 6 Review
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Regents Geometry Ch. 6 Review
01/21/2014
1.
Answer:
C
20.
Answer:
B
2.
Answer:
B
21.
Answer:
75
3.
Answer:
C
22.
Answer:
102
4.
Answer:
B
23.
Answer:
D
24.
Answer:
D
25.
Answer:
15
26.
Answer:
18
27.
Answer:
(10; 20)
28.
Answer:
B
29.
Answer:
6
30.
Answer:
A
31.
Answer:
C
32.
Answer:
B
33.
Answer:
13.9
34.
Answer:
C
35.
Answer:
C
36.
Answer:
C
37.
Answer:
D
38.
Answer:
C
39.
Answer:
C
5.
Answer:
An interior angle of 108 and an exterior
angle of 72
6.
Answer:
A
7.
Answer:
A
8.
Answer:
A
9.
Answer:
D
10.
Answer:
A
11.
Answer:
C
12.
Answer:
C
13.
Answer:
A
14.
Answer:
110
15.
Answer:
35
16.
Answer:
D
17.
Answer:
11
18.
Answer:
17
19.
Answer:
120
Teacher's Key
40.
Answer:
A
41.
Answer:
C
42.
Answer:
A
43.
Answer:
D
44.
Answer:
B
45.
Answer:
D
46.
Answer:
D
47.
Answer:
D
48.
Answer:
A
49.
Answer:
84
50.
Answer:
100
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