Download Lekcja 4 A

SJO PW - Język angielski ogólnotechniczny, Poziom B2
Lekcja 4 A
Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyła, E. Fronc
______________________________________________________________________________________________
GEOMETRY AND MEASUREMENT
Geometric Figures – Two-Dimensional Geometry
Task 1.
Point and lines, angles, triangles, quadrilaterals, polygons, and the circle
i.
Point and Lines:
Read the following sentences and choose the appropriate word in each pair.
A straight line is a particular set/combination of points.
Two lines which lie in the same plane and which do not intersect, i.e. they do not share one common point are called
perpendicular/parallel lines. They remain the same distance apart at all times.
Two lines that intersect and form right angles are called perpendicular/parallel lines.
ii.
Angles:
Look at the attached glossary and match the name to the angle.
a) An obtuse angle
b) A right angle
c) An acute angle
1.___
2.___
3.___
Triangles
ABC is a triangle. It has three equal angles and three equal sides.
A triangle that has three equal sides is called an equilateral triangle.
ABC is an isosceles triangle. It has two equal sides (AC and CB). When a triangle has two equal sides then it also has
two equal angles.
All triangles can be classified into three categories: acute (-angled) triangles, obtuse (-angled) triangles, right (-angled)
triangles.
Two triangles may be called similar only if their corresponding angles are congruent and their corresponding sides are
proportional in length.
iii.
Quadrilaterals and Polygons
Polygons can be divided into regular polygons (when a polygon has all sides and all angles equal), and irregular
polygons. We can also describe polygons as convex or concave. A convex polygon is a polygon that has all interior
angles less than 180°. A polygon that has one or more interior angles greater than 180° is concave.
iv.
The Circle:
Choose the correct word in each pair.
All points on the circle are equidistant from the centre. The distance across a circle through the centre is called
the diameter / radius. The diameter / radius of a circle is the distance from the centre of a circle to any point of the
circle. The diameter / chord of a circle is twice as long as the radius – so it is as long as two radii. The diameter /
chord is a line segment that joins two points on a curve. A circle can have many different diameters / chords – but if
the diameter / chord passes through the centre it is called the diameter / chord / radius. The area of a circle equals πr2
where r is the radius The perimeter of a circle is called the circumference. The circumference is calculated by the
formula C=2πr, where r is the radius.
Task 2.
Match the angle names a, b, c to their descriptions 1, 2, 3
a. A right angle
1. It measures more than 0O but less than 90O. (90 degrees)
b. An acute angle
2. It measures more than 90O and less than 180O.
c. An obtuse angle
3. It measures 90O.
Task 3.
Choose the word in italics that fits the following sentences describing pictures on the right.
ABC here is a/an acute/obtuse/right triangle because all the angles are acute/obtuse.
ABC is a/an acute/obtuse/right triangle because one of its angles is a right angle.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Lekcja 4 A
Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyła, E. Fronc
______________________________________________________________________________________________
ABC is a/an acute/obtuse/right triangle because one of its angles is an obtuse/acute angle.
In a right (-angled) triangle, the side opposite the right angle is called the hypotenuse and the other two sides are called
the legs. If c represents the length of the hypotenuse and if a and b represent the length of the legs, then c2=a2+ b2
(which reads: c squared equals a squared plus b squared). This is Pythagorean Theorem, which states that in any right
triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Match the name to the figure: square, hexagon, pentagon
Task 4.
a)__________
b)__________
c)___________
These are examples of some regular polygons. A polygon which has four sides only is called a quadrilateral. The
rectangle, the trapezium and the rhombus are examples of quadrilaterals.
Task 5.
1.
2.
3.
4.
5.
Decide if the following sentences are true or false:
A rectangle is a quadrilateral that has four equal angles.
A square can be described as a rectangle that has two adjacent sides of equal length.
All quadrilaterals are polygons.
All polygons are quadrilaterals.
If each angle of a rhombus is 90 degrees, it is a square.
Geometric Figures – Three-Dimensional Geometry
3-D geometry is the geometry of three-dimensional space. It is called three dimensional, or 3-D, because there are
three dimensions: width, depth and height. There are two main types of solids (3-D shapes): polyhedra and nonpolyhedra, (singular – polyhedron, plural –polyhedra/polyhedrons). Polyhedra have flat faces.
Match the name to the solid: cube, cuboid, pyramid, prism, cone, cylinder, sphere, torus (pl. tori)
Task 6.
1._______
2._______
5._______
3.________
6.________
7.________
Weights and Measures
Task 7.
Weight
1 gram (g) = 0.001 kilogram (kg)
The weights in the table are mixed. Match the metric values to their GB&US equivalents:
UK&US
1 ounce (oz)
1 pound (lb)
= 16 ounces (oz)
1 stone
= 14 pounds (lb)
1 US Short ton = 2,000 pounds (lb)
1 UK Long ton = 2,240 pounds (lb)
2,204.6 pounds (lb)
Task 8.
long – length
Metric
1,016.04 kilograms
28.350 grams
0.454 kilograms (kg)
6.35036 kilograms
1 tonne (t) = 1,000 kg
907.184 kg
Length, area, volume, liquid: capacity/volume
deep – depth wide – width heavy – weight
2
tall / high - height
4._______
8._______
SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyła, E. Fronc
Lekcja 4 A
______________________________________________________________________________________________
i. Length:
Complete the lengths table below by writing the missing values.
1 milimetre (mm) = 0.001 metre (m)
1 centimetre (cm) = 0.01 m
1 kilometre (km) = 1,000 m
UK&US
Metric
1 inch (in) 1’’
25.39 milimetres (mm)
1 foot (ft) 1’ = _____ inches (____’’)
30.479 centimetres (cm)
1 yard (yd) = _____ feet
0.914 metres (m)
1 mile (mi) = _____ yards
1.609 kilometres (km)
1 sea (or nautical) mile
1.852 kilometres
ii. Area
1 square metre (m²) = 1m x 1m (1 metre by 1 metre)
1 square millimeter (mm²)
iii. Volume
1 cubic metre (m³) = 1m x 1m x 1m
1 cubic centemetre (cc) = 1cm x 1cm x 1cm
iv. Liquid – capacity/volume
1 litre (l) = 0.001 m³
UK
US
Metric
1 pint (pt)
1.201 pints
0.5679 litres (l)
1 gallon (UK - gal) = 8 pt 1.201 US gal
4.54609 litres
1 liquid galon/1 dry gallon 3.785411784 litres / 4.40488377086
Task 9.
Temperature:
What do the following values represent? Complete the table below with the
phrases from the list: freezing point, boiling point, absolute zero, room temperature, blood heat:
Fahrenheit (ºF)
Centigrade (ºC ) – degree Celsius
212
100
194
90
98.6
37
64.5
18
32
0
0
-17.8
-459.67
-273.15
Task 10.
Do the crossword below.
Across
Down
3. cięciwa
1. przeciwprostokątna
6. wielokąt
7. czworokąt
2. kąt
8. promień
9. trójkąt
4. średnica
10. przyprostokątna
11. równoboczny
5. okrąg
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyła, E. Fronc
Lekcja 4 A
______________________________________________________________________________________________
Task 11.
Which is greater?
a) 7 pt or 3 l
f) 212F or 212C
b) 3 gal or 15 l
g) 1 oz or 30 g
c) 1 mi or 1 km
h) 2 lb or 1 kg
d) 1 yd or 4 ft
i) 1 ton or 1 tonne
e) 10 m or 10 yd
Task 12.
Complete the following sentences using appropriate words from the list below (one word may be used
more than once):
diameter, deep, depth, long, length, wide, width, weigh, heavy, weight, tall, high, height
1.
The highway from Warsaw to Cracow is about 500 kilometres in _________.
2.
What is the ___________ of the highest mountain in Poland?
3.
They couldn’t get the piano through the door because of its ___________.
4.
Draw a circle which is 10 centimetres in ____________.
5.
The ___________ of the Śniardwy Lake at its deepest point is 23.4 m.
6.
They hung a picture at a ____________ of 6 feet above the ground.
7.
This parcel is very heavy. What is its __________?
Task 13.
Answer the following questions.
a)
In the UK I was told my friend weighed 10 stone 10 pounds. What is her weight in kg?
b)
If the speed limit in Warsaw is 50 kms/h, what speed is the speed in mp/h?
c)
A bath has hot and cold-water taps which admit 30 litres and 40 litres per minute. The bath holds 500 litres. If
both taps are turned on, how many litres would flow in per minute? How long will the bath take to fill?
d)
If you want to convert Centigrade temperature into Fahrenheit, multiply by 9/5 (nine/fifths) and add 32. What
is the outside temperature now? What was it at the weekend? Give the answers in Celsius and Fahrenheit.
Read the result aloud.
REFERENCES:
1. Słownik naukowo-techniczny, Wydawnictwa Naukowo – Techniczne, 1998
2. Ibbotson Mark, Professional English in Use – Engineering, Cambridge 2009
3. Krukiewicz-Gacek Anna, Trzaska Agnieszka, English for Mathematics, AGH University of Science and
Technology Press Kraków 2010
4. Szkutnik Leon Leszek, An Introductory Course in Scientific English, PWN 1979
5. Szyke Grażyna, What, Why & How in the World of Science, WSiP, 1986
6. Discovery Puzzlemaker
7. The Internet
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