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4] In ∆ LMN, mL = 80°, mN = 70°, then mM = ……..
i) 50°
ii) 20°
iii) 70°
iv) 30°
The Mathematics Department
Stage : 1st Prep
Date
: /
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2nd Term
Mid Year Revision
Polygon & Quadrilateral
5] The polygon which has no diagonals is …………………
i) a pentagon
ii) a quadrilateral
iii) a triangle
iv) a hexagon
[1] Complete the statements of group (A) with the
suitable statements in group (B):
Group (A)
1] In a parallelogram
……c….
Group (B)
a) The two diagonals are equal in
length and not perpendicular.
2] In a rhombus
……………e…………
b) The two diagonals are equal in
length and perpendicular.
3] In a rectangle
……………a………
c) The two diagonals bisect each
other.
4] In a square
……………b…………
d) There are two opposite sides
parallel and not equal.
5] In a trapezium
…………d…..…
e)
6] ABC is a triangle, if mA = mB = 30°, then mC = ……..
i) 30°
ii) 60°
iii) 120°
iv) 150°
7] The sum of measures of the interior angles of a triangle is
………….
i) 180°
ii) 90°
iii) 360°
iv) 108°
8] The sum of the measures of the interior angles of a polygon
of 6 sides is ……
i) 120°
ii) 360°
iii) 540°
iv) 720°
The
two
diagonals
are
perpendicular and not equal in
length.
9] The regular pentagon whose side is of length 4 cm, its
perimeter is …. cm.
i) 20
ii) 16
iii) 32
iv) 25
10] 30°, 70° and ……. could be the measures of the three angles
of a triangle.
i) 30°
ii) 70°
iii) 80°
iv) 180°
[2] Choose the correct answer:
1] The measure of the regular pentagon angle is ………….
i) 180°
ii) 118°
iii) 120°
iv) 108°
2] The measure of each angle of a regular hexagon ……….
i) 180°
ii) 720°
iii) 120°
iv) 108°
11] The equilateral triangle is a regular polygon of three sides,
hence the measure of each angle of it = ………
i) 30°
ii) 60°
iii) 90°
iv) 120°
3] If the perimeter of an equilateral triangle is 12 cm, then the
length of its side is …….. cm.
i) 3
ii) 4
iii) 6
iv) 36
12] In the square, all angles are ………..
i) acute
ii) right
iii) obtuse
1
iv) straight
13] ABCD is a parallelogram, if mA = 90°, then ABCD is a ……
i) square
ii) rhombus iii) rectangle
iv) triangle
21] If XYZL is a parallelogram such that mX = mY, then XYZL
is a …….
i) square
ii) rhombus iii) rectangle
iv) trapezium
14] In the parallelogram, the diagonals are ………..
i) equal in length
ii) perpendicular
iii) bisect each other
iv) parallel
22] The diagonals of the rectangle are …………………
i) perpendicular
ii) parallel
iii) equal in length
iv) bisect each opposite angles
15] ABCD is a quadrilateral such that AB // CD and AB ≠ CD,
then it will be a …
i) rhombus
ii) trapezium iii) rectangle
23] If two adjacent sides in a parallelogram are equal in length,
then the figure is a …………….
i) square
ii) rhombus iii) rectangle
iv) trapezium
iv) square
16] The quadrilateral whose two diagonals are equal in length
and not perpendicular to each other is a ……………
i) rhombus
ii) trapezium
iii) rectangle
iv) square
24] The diagonal bisects the two opposite angles for the ………….
i) parallelogram
ii) rhombus
iii) rectangle
iv) trapezium
17] If ABCD is a rhombus, mB = 100°, then mBDC = ………
i) 110°
ii) 80°
iii) 40°
iv) 50°
25] The square is ………..…. with a right angle.
i) square
ii) rhombus iii) rectangle
iv) trapezium
18] The diagonals of the ………….. are perpendicular and not
equal in length.
i) square
ii) parallelogram
iii) rectangle
iv) rhombus
26] If the diagonals of the rectangle are perpendicular, the it is
a ………..
i) trapezium ii) parallelogram
iii) rhombus iv) square
19] In a parallelogram, any two consecutive angles are ………..
i) supplementary
ii) complementary
iii) equal in measure iv) the sum of their measures is 360°
27] The diagonal of the square makes with its side an angle of
measure ………
i) 60°
ii) 45°
iii) 30°
iv) 90°
20] If two diagonals of a parallelogram are perpendicular and
equal in length, then it is a ………….
i) square
ii) rhombus iii) rectangle
iv) trapezium
28] ABCD is a parallelogram in which mA + mC = 160°, then
mB = …………
i) 110°
ii) 80°
iii) 20°
iv) 100°
2
[3] Complete:
1] The sum of the measures of the interior angles of a triangle =
…180…… °
15] A parallelogram in which its two diagonals are perpendicular
and not equal in length is a ………………….
2] The measure of the exterior angle of an equilateral triangle
equals …120°…
16] If ABCD is a parallelogram such that mA = 65°, then mB
= …115….. °
5] ABCDE is a pentagon, mA = mB = 90°, mC + mD =
280°, then mE = …80.. °
17] The rhombus such that one of its angles is right is a
………square….
6] In ∆ LMN, if mL = 35°, mM = 60°, then mN = …85… °
18] The diagonal of the square makes with its side an angle of
measure ……45… °
7] The two diagonals of the rhombus are …bisect each other..
, ……perpendicular…..
19] A quadrilateral with exactly one pair of parallel sides is a
……trapezium…….
8] The two diagonals of the rectangle are …equal in length…
20] The length of one side of a rhombus is 5 cm, then its
perimeter = …20… cm.
9] The sum of measures of two consecutive angles of a
parallelogram = ……180°..
[4] In the opposite figure:
If mE = mF
Find mE
10] If the two diagonals of the rhombus are equal in length,
then it is a ……square…..
F
•
A
130°
E
•
Solution:
The sum of measures of angles of 6
sides polygon = (6 – 2)  180 = 720°
mE + mF = 720° - (130° + 125° + 120° + 127°)
= 218°
mE = mF = 218 ÷ 2 = 109°
11] The ……rhombus… is a parallelogram with two adjacent
sides equal in length.
12] ABCD is a rhombus, then AC …….. BD
13] In a parallelogram, every two opposite sides are …equal…
and ……parallel……
14] The parallelogram which its diagonals are equal in length
and perpendicular is a ……square……
3
125°
127°
D
120°
C
B
[5] In the opposite figure:
D
AD // BE , mE = 70°,
BD

C
B
mC = 105°. Find: mB
Solution:
∵ EFD is an equilateral triangle
∴ mEDF = 60°
50°
F
DF = {C}
mBCD = mECF = 60°
∵ BD
(V.O.A)
mD + mBCD = 180°
(interior angles)
mD = 180° - 60° = 120°
mD = mA = 120°
In the quadrilateral ABCD
mB = 360° - (120° + 120° + 60°) = 60°
A
120°
E
B
//
D
105°
C
F
AC = {D}
∴ mADC = mEDF = 60°
(V.O.A)
In the quadrilateral ABCD
mB = 360° - (120° + 105° + 60°) = 75°
AD // BE , DF is a transversal
M
AC = {D}, mA = 120°
A
//
BE
•
[7] In the opposite figure:
EFD is an equilateral triangle,
A
//
mF = 50° and mD = mA
E
70°
Find: m B.
Solution:
In ∆ CEF:
mECF = 180° - (70° + 50°) = 60°
•

[8] In the opposite figure:
mABC = 110°, mCBD = 35°
C
and mABE = 140°
D
Find: mEBD
Proof:
∵mEBD + mABE + mABC + mCBD = 360°
∴mEBD = 360° - (140° + 110° + 35°) = 75°
B
[6] In the opposite figure:
ABCDEF is a regular hexagon,
F
mN = 29°.
Find: mM.
N
Solution:
E
D
ABCDEF is a regular hexagon
(6 - 2)  180
m (AFE) =
= 120
6
m (MFN) = m (AFE) = 120°
(V.O.A)
In ∆ FMN : m (M) = 180 – (120 + 29) = 31°
35°
110°
B 140°
A
E
C
[9] In the opposite figure:
ABCD is a parallelogram,
mBDC = 44, mDBC = mC
Find mA
A
In BCD
mC = mDBC , mBDC = 44
mDBC + mC = 180 – 44 = 136
m C = 136  2 = 68
ABCD is a parallelogram
mA = mC = 68
4
D
C
●
44°
●
B
[10] In the opposite figure:
EF intersects AB & CD at X
& Y respectively, mAXE =
mDYF = 75°
Prove that: AB // CD
∴ ACED is a rectangle
E
75°
B
X
D
A
75° Y
F
[13] In the opposite figure:
C
AC // DH
1] Prove that: ACHD is a parallelogram
2] Find m (H)
Solution:
H
∵ ABCD is a square
Solution:
mBXY = mAXE = 75° Vertically opposite angles
mDYF = 75°
∴ mBXY = mDYF
∵BXY &DYF are equal in measure and corresponding
AB // CD
[11] In the opposite figure:
D
ABCD is a rhombus, in which BD is a
diagonal and mABD = 70°.
Find with proof mA
∵ ABCD is a rhombus, BD is a diagonal in it
∴ mABC = 2 mABD = 2 × 70° = 140°
∴ mA = 180° - 140° = 40°
C
70°
B
A
//
∴ AD // BC & AD = BC
∵ BC = EC
E
D
∴ AD // CE & AD = CE
∴ ACED is a parallelogram
∵ AC  BC
∴ AB // BC
AB // CH
∵ AC // DH
∴ ACHD is a parallelogram

∵ AC is a diagonal in the square ABCD
∴ mCAD = 45°
In the parallelogram ACHD
mH = mCAD = 45°
(opposite angles)
A
//
B
[12] In the opposite figure:
ABCD is a parallelogram,
AC  BC . E  BC where BC = EC
Prove that: ACED is a rectangle
■
C
Solution:
∵ ABCD is a parallelogram
D
ABCD is a square, H  BC and
∴ mACE = 90°
5
A

C
■B