Download chapter 10: polygons

POLYGONS (Chapter 10)
Mathematics for Australia Year 7 - Homework
CHAPTER 10: POLYGONS
10A
c
POLYGONS
d
REMINDER
A polygon is a closed plane figure with straight line sides
which do not cross over.
4 Draw a freehand sketch of:
a a convex 5-sided polygon
1 Which of these figures can be classified as a polygon?
Give a reason if the figure is not a polygon.
a
b a non-convex quadrilateral
b
c
REMINDER
A regular polygon has all sides of equal length and all
angles of equal measure.
d
5 Explain why these figures are not regular polygons:
a
e
b
2 What special name is given to a polygon with five sides?
REMINDER
A convex polygon is a polygon with no interior reflex
angles.
6
a Draw a freehand sketch of a convex hexagon, and
draw all of its diagonals.
3 Name these polygons according to their number of sides
and whether they are convex:
a
b
b How many diagonals does a hexagon have?
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Mathematics for Australia Year 7 - Homework
10B
POLYGONS (Chapter 10)
b
TRIANGLES
REMINDER
A triangle is:
² equilateral if its sides are all equal in length
² isosceles if at least two of its sides are equal in length
² scalene if none of its sides are equal in length.
c
1 Measure the lengths of the sides of these triangles.
Use your measurements to classify each as equilateral,
isosceles, or scalene.
a
3 The following diagrams are not drawn to scale, but the
information marked on them is correct. Classify each
triangle using at least two descriptive words.
a
b
b
c
c
REMINDER
A triangle is:
² acute angled if all of its angles are acute
² right angled if one of its angles is a right angle (90± )
² obtuse angled if one of its angles is obtuse.
d
2 Measure the sizes of the angles of these triangles. Use
your measurements to classify each as acute, obtuse, or
right angled.
a
10C
ANGLES OF A TRIANGLE
REMINDER
The sum of the angles in a triangle is 180± .
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POLYGONS (Chapter 10)
Mathematics for Australia Year 7 - Homework
1 Find x in the following:
a
3 Find the unknowns in these triangles, giving brief reasons
for your answers:
a
35°
x°
70°
a°
65°
a°
b
x°
b
136°
62°
b°
b°
c
64°
c
x°
52°
3c°
2c°
c°
REMINDER
The exterior angle of a triangle is equal to the sum of the
two interior opposite angles.
4 Find x in the following:
a
a°
x°
b°
56°
x± = a± + b±
(x + 12)°
2 Find x in the following:
a
x°
b
74°
86°
x°
2x°
b
(x - 15)°
c
32°
x°
106°
x°
(x + 10)°
c
(3x - 25)°
x°
118°
139°
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Mathematics for Australia Year 7 - Homework
10D
POLYGONS (Chapter 10)
f
ISOSCELES TRIANGLES
23°
REMINDER
x°
An isosceles triangle has at least two sides equal in length.
In any isosceles triangle:
² the base angles are equal
² the line joining the apex
to the midpoint of the
base is perpendicular to
the base.
2 In each of the following triangles, find the value of x.
Hence deduce something about the triangle.
a
A
38°
B
1 Find the unknowns in the following which have not been
drawn to scale:
a
(2x + 28)°
x°
C
46°
b P
x°
Q
3x°
126°
4x°
b
R
x°
40°
10E
c
REMINDER
x cm
4 cm
QUADRILATERALS
A quadrilateral is a polygon with four sides.
50°
50°
1 Match each quadrilateral name with the most appropriate
description.
parallelogram
d
rectangle
#bluebox#22.79651#6.72481
square
x°
#bluebox#12.45361#5.90108
rhombus
#bluebox#16.15866#6.72481
trapezium
#bluebox#17.33247#6.72481
#bluebox#15.58206#6.72481
kite
#bluebox#8.55122#6.72481
a A .................................. is a quadrilateral which has
exactly one pair of opposite sides parallel.
118°
b A .................................. is a quadrilateral in which
all sides are equal.
c A .................................. is a quadrilateral which has
two pairs of adjacent sides equal.
e
8 cm
x°
75°
d A .................................. is a quadrilateral which has
opposite sides parallel.
y cm
e A .................................. is a quadrilateral in which
all angles are equal and all sides are equal.
f A .................................. is a quadrilateral in which
all angles
equal.
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POLYGONS (Chapter 10)
Mathematics for Australia Year 7 - Homework
2 Draw a fully labelled sketch of a rectangle.
6 Draw a diagram to fit the following instructions. Make
sure you label all of the given information.
ABC is a triangle where [BC] is 8 cm long, [AB] is 6 cm
long, and [AB] ? [BC].
3 True or false? Explain your answer.
a All squares are rhombuses.
b There are no rectangles which are also kites.
7 Find the values of the variables in these figures, giving
reasons for your answers:
a
x cm
5 cm
y cm
4 Use a ruler to help classify the following:
a
12 cm
b
b
y°
x°
REMINDER
k reads is parallel to.
10F
ANGLES OF A QUADRILATERAL
? reads is perpendicular to.
5 Using ? and k, write two statements about the following
figure:
A
REMINDER
The sum of the angles of a quadrilateral is 360± .
B
a°
d°
D
C
61 5
b°
c°
a + b + c + d = 360
Mathematics for Australia Year 7 - Homework
POLYGONS (Chapter 10)
1 Find the values of the variables, giving brief reasons for
your answers:
a
46°
76°
124°
x°
2 Consider the following
diagram:
c°
a° 82°
b°
115°
a Find the values of a and b.
89°
b
75°
b Hence find the value of c.
b°
b°
c
61°
c°
58°
132°
c°
REVIEW OF CHAPTER 10
1 Which of these figures can be classified as a polygon?
d
d°
a
d°
2d°
b
c
2d°
2 Use a ruler and protractor to completely classify the
following triangle. You should have two descriptions.
e
b°
127°
127° a°
f
111°
60°
b°
87°
3 Find, giving reasons, the value of x:
a
a°
51°
63°
61 6
x°
POLYGONS (Chapter 10)
Mathematics for Australia Year 7 - Homework
7 Using the information on the diagram, name the figure
and find the values of c and d.
b
115°
x°
d°
98°
70°
c°
c
x°
113°
8 Find the values of a and b in this figure, giving reasons
for your answer.
86°
d
50°
a°
x°
b°
91°
79°
e
x°
74°
4 Find the value of x, and hence classify triangle PQR.
R
x°
(x - 42)°
P
74°
Q
5 Can a parallelogram be a kite? Explain your answer.
6 Find the values of a and b.
24°
a° b°
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