Download Polygons and Circles

Grade 7
Mathematics: Geometry
Polygons and Circles
Question 1:
Multiple Choice
(5)
1.1
Which one of the following statements is FALSE?
A
A right-angled triangle cannot have an obtuse angle.
B
All squares are rectangles.
C
Co-interior angles are always equal.
D
All rectangles are parallelograms.
1.2
Which polygons fit the following description?
Two opposite angles are equal, diagonals bisect at a right angle.
A
rhombus and parallelogram
B
rhombus and a square
C
rectangle and parallelogram
D
square and rectangle
1.3
A closed shape with seven sides, not all equal, is a/an:
A
irregular heptagon
B
irregular hexagon
C
regular heptagon
D
regular hexagon
1.4
Which two shapes will be formed if one diagonal line is drawn inside a square?
A
equilateral triangles
B
acute-angled triangles
B
right-angled scalene triangles
D
right-angled isosceles triangles
1.5
Which of the following describes an isosceles trapezium?
A
Two pairs of parallel and equal sides
B
One pair of parallel sides and another pair of equal sides
C
One pair of parallel and equal sides
D
Two pairs of parallel sides and one pair of equal angles
Question 2:
Match Column A to Column B
Column A
Answer
(8)
Column B
2.1 congruent triangles
A Two pairs of parallel sides, opposite angles equal
2.2 kite
B No angles or sides are equal
2.3 pentagon
C Angles are equal, length of sides are different
2.4 similar triangles
D Angle greater than 1800
2.5 trapezium
E Corresponding angles and sides are equal
2.6 scalene triangle
F Interior angles measuring 1080 each
2.7 parallelogram
G Diagonals cross at a 900 angle
2.8 reflex angle
H One pair of parallel sides
Page 1 of 13
Grade 7
Mathematics: Geometry
Polygons and Circles
Question 3: Construct and name the following angles.
3.1
∠ABC = 2980
Question 4:
3.2
(4)
∠DEF = 1150
Circles
4.1
Construct a circle with a diameter of 5cm.
(2)
4.2
Draw in a radius, separate from the diameter and show the measurement.
(1)
4.3
Draw and label a chord.
(1)
4.4
What is the section between the two radii called?
4.5
What is the difference between a radius and a chord?
_____________________
(1)
(2)
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
4.5
Use a green pen to show the circumference.
Page 2 of 13
Grade 7
Mathematics: Geometry
Polygons and Circles
>
Question 5: Constructing polygons
Draw line segment AB = 6 cm. Construct line BC = 4 cm, with ABC = 650. Construct line
>
5.1.1
CD ll AB, where CD = 6 cm and BCD = 1150. Connect point D and A.(Remember to show
all symbols and measurements)
(6)
Classify shape ABCD
_________________________________
5.2.1
Construct polygon EFGH, where line EF = FG = 30 mm and EFG = 750. Draw line
(1)
>
>
>
5.1.2
GH = EH = 50 mm and FEH = FGH = 1200. Connect point E to point G with a straight line.
Construct a perpendicular bisector of line EG, through point I,
connecting point F and H.
(7)
Page 3 of 13
Grade 7
Mathematics: Geometry
Polygons and Circles
5.2.2
Classify polygon EFGH.
________________________________________ (1)
5.2.3
Classify △EFI
________________________________________ (2)
5.2.4
Classify △EFG
________________________________________ (1)
5.2.5
Calculate the size of ∠FGE , with a reason.
(2)
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Question 6: Calculate the value of the angles, with reasons, as requested:
6.1
Calculate the values of
x
and
y:
(4)
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Page 4 of 13
Grade 7
Mathematics: Geometry
Polygons and Circles
6.2
ABCD is a parallellogram. Calculate the value of
w, x, y, z :
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Page 5 of 13
Mathematics: Geometry
6.3
Grade 7
Find the values of all the variables:
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
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_____________________________________________________________________________
_____________________________________________________________________________
Question 7: Perimeter
7.1
A number of identical circles are tightly packed inside a rectangle. The radius of one circle
is 3,5 metres. What is the perimeter of the rectangle into which the circles are packed? (3)
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
_____________________________________________________________________________
Page 6 of 13
Grade 7
Mathematics: Geometry
Polygons and Circles
7.2.1
Find the value of
x , if the perimeter of the shape is 44,5 cm:
(3)
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7.2.2
Give the perimeter in metres.
________________________________________ (1)
7.2.3
Classify the polygon.
________________________________________ (1)
7.3
There are six identical squares in this shape. The perimeter of one square is 1 800 cm.
7.3.1
Find the perimeter of the shape.
(2)
___________________________________________
___________________________________________
___________________________________________
___________________________________________
___________________________________________
7.3.2
Give the perimeter in kilometres.
(1)
___________________________________________
7.3.3
Which 3-D shape will be formed if this shape is
folded?
(1)
___________________________________________
Page 7 of 13
Grade 7
Mathematics: Geometry
MEMO:
Question 1:
Multiple Choice
(5)
1.1
Which one of the following statements is FALSE?
A
A right-angled triangle cannot have an obtuse angle.
B
All squares are rectangles.
C
Co-interior angles are always equal. (Co-interior angles add up to 1800)
D
All rectangles are parallelograms.
1.2
Which polygons fit the following description?
Two opposite angles are equal, diagonals bisect at a right angle.
A
rhombus and parallelogram
B
rhombus and a square
C
rectangle and parallelogram
D
square and rectangle
1.3
A closed shape with seven sides, not all equal, is a/an:
A
irregular heptagon
B
irregular hexagon
C
regular heptagon
D
regular hexagon
1.4
Which two shapes will be formed if one diagonal line is drawn inside a square?
A
equilateral triangles
B
acute-angled triangles
B
right-angled scalene triangles
D
right-angled isosceles triangles
1.5
Which of the following describes an isosceles trapezium?
A
Two pairs of parallel and equal sides
B
One pair of parallel sides and another pair of equal sides
C
One pair of parallel and equal sides
D
Two pairs of parallel sides and one pair of equal angles
Question 2:
Math Column A to Column B
(8)
Column A
Answer
Column B
2.1 congruent triangles
E
A Two pairs of parallel sides, opposite angles equal
2.2 kite
G
B No angles or sides are equal
2.3 pentagon
F
C Angles are equal, length of sides are different
2.4 similar triangles
C
D Angle greater than 1800
2.5 trapezium
H
E Corresponding angles and sides are equal
2.6 scalene triangle
B
F Interior angles measuring 1080 each
2.7 parallelogram
A
G Diagonals cross at a 900 angle
2.8 reflex angle
D
H One pair of parallel sides
Page 8 of 13
Grade 7
Mathematics: Geometry
Question 3: Construct and name the following angles.
3.1
∠ABC = 2980
3.2
(4)
∠DEF = 1150
620
Reflex angle (Remember when constructing a
reflex angle use 3600 - angle, then measure the
acute angle first)
Question 4:
Obtuse angle
Circles
4.1
Construct a circle with a diameter of 5cm.
(2)
4.2
Draw in a radius, separate from the diameter and show the measurement.
(1)
4.3
Draw and label a chord.
(1)
4.4
What is the section between the two radii called?
4.5
What is the difference between a radius and a chord?
Sector
(1)
(2)
A radius is the straight line from the centre of the circle to any point on the circumference.
A chord is a straight line connecting any two points on the circumference of a circle, but not
through the centre of the circle.
4.5
Use a green pen to show the circumference.
(1)
Page 9 of 13
Grade 7
Mathematics: Geometry
>
Question 5: Constructing polygons
Draw line segment AB = 6 cm. Construct line BC = 4 cm, with ABC = 650. Construct line
>
5.1.1
CD ll AB, where CD = 6 cm and BCD = 1150. Connect point D and A.(Remember to show
all symbols and measurements)
(6)
(Not drawn to scale, remember all symbols and measurements)
Classify shape ABCD
Parallelogram
(1)
5.2
Construct polygon EFGH, where line EF = FG = 30 mm and EFG = 750. Draw line
>
>
>
5.1.2
GH = EH = 50 mm and FEH = FGH = 1200. Connect point E to point G with a straight line.
Construct a perpendicular bisector of line EG at point I , connecting point F and H.
(7)
(Not drawn to scale, remember all symbols and measurements)
I
Page 10 of 13
Grade 7
Mathematics: Geometry
5.2.2
Classify polygon EFGH.
kite
(1)
5.2.3
Classify △EFI
right-angled scalene triangle
(2)
5.2.4
Classify △EFG
isosceles triangle
(1)
5.2.5
Calculate the size of ∠FGE , with a reason.
∠FGE = (180° − 75°) ÷ 2
∠FGE = 52,5°
(1)
Two angles of an isosceles triangle is equal.
Question 6: Calculate the value of the angles, with reasons, as requested:
6.1
Calculate the values of
x
and
y.
(4)
600
220
1200
600
600
TIP: Write everything you know onto the drawing, e.g. equilateral triangle - all angles equal 600
before you start. Then write each angle you solve onto the drawing.
Supplementary angles equal 1800
∠DBC = 180° − 158° = 22°
Equilateral triangle - All angles are equal to 600
∠CDE = 60°
Supplementary angles equal 1800
x = 180° − 60° = 120°
y = 180° − 120° − 22° = 38°
Inner angles of a triangle add up to 1800
6.2
w, x, y, z :
ABCD is a parallellogram. Calculate the value of
(4)
>>
>>>
>>>
450
600
>>
450
First add in everything you know!
w = 180° − (90° + 45°) = 45°
Inner angles of a triangle add up to 1800
z = 45°
∠BHA = 90°
y = 180° − (90° + 30°) = 60°
Alternate angles are equal
x = 60°
Opposite angles of a parallellogram is equal
Supplementary angles add up 1800
Inner angles of a triangle add up to 1800
Page 11 of 13
Grade 7
Mathematics: Geometry
6.3
Find the value of all the variables:
(7)
b = 85°
Vertically opposite angles
f = 85°
Coordinating angles
d = 85°
Vertically opposite angles
h = 180° − 85° = 95°
Co-interior angles
a = 95°
Alternate angles
g = 95°
Coordinating angles
e = 95°
Alternate angles
There may be more than one way to
get to the answers.
Remember: No reason, no mark!
Question 7: Perimeter
7.1
A number of identical circles are tightly packed inside a rectangle. The radius of one circle
is 3,5 metres. What is the perimeter of the rectangle into which the circles are packed? (3)
Diameter of one circle: 3,5 m x 2 = 7 m
Length of rectangle = 7 m x 5 = 35 m
Breadth of rectangle = 7 m x 3 = 21 m
Perimeter = 2ℓ + 2b = (2 x 35 m) + (2 x 21 m) = 112 metres
Page 12 of 13
Grade 7
Mathematics: Geometry
7.2.1
Find the value of
x , if the perimeter of the shape is 44,5 cm:
(3)
x + x + 2x + 7, 3cm + 9cm + 3cm + 8, 4cm = 44,5cm
4x + 30,9 = 44,5cm
4x = 13,6cm
x = 3, 4cm
7.2.2
Give the perimeter in metres.
44,5 cm = 0,445m
(1)
7.2.3
Classify the polygon.
Irregular octagon
(1)
7.3
There are six identical squares in this shape. The perimeter of one square is 1 800 cm.
7.3.1
Find the perimeter of the shape.
(2)
One side of the square = 1800cm ÷ 4 = 450cm
Perimeter = 14 × 450cm = 6300cm
7.3.2
Give the perimeter in kilometres.
(1)
6 300 cm = 63 m = 0,063 km
7.3.3
Which 3-D shape will be formed if this shape is
folded?
(1)
A cube
Page 13 of 13