16. Underline the correct tense form in the following sentences.

1. If his car breaks / will break down, he calls the auto club.

2. You will be able to see / are able to see better if you turn on the lamp.

3. You'll pay higher insurance if you will buy / buy a sports car.

4. You won't pass the course if you won't study / don't study.

5. When I get / will get a letter, I usually write back immediately.

6. If I will be / am in Venice, I will rent a boat.

7. If we surf / will surf the Internet, we will find a lot of information.

17. Put the verbs in brackets in the correct tense. Add a comma where necessary.

1. Please call me if you ….. (to need) any help.

2. If he ….. (to arrive) on time we’ll discuss our plans before we go out.

3. She won’t go to Australia unless I ….. (to pay) for her tickets.

4. ….. she ….. (to be) angry if we don’t go to the meeting?

5. If you ….. (to work) hard you may be promoted.

6. If you help me I ….. (to repair) it.

7. If you leave now you ….. (to get) there before it closes.

Unit 15 geometric figures

LEAD-IN

1. Match the geometric figures to their names.

1	2	3	4	5	6	7	8
A Square	B Rectangle	C Arc	D Triangle	E Hexagon	F Cylinder	G Circle	H Cube

2. What other geometric figures do you know? Name the objects in the classroom that have the shape of a circle, triangle, square, rectangle, oval, arc, cube, cylinder, hexagon, etc.

READING

3. Read the text and correct the statements that follow. Geometric Figures

Geometry is the mathematical study of shapes, figures, and solids. Circles, triangles, and squares, rectangles, parallelogram are some of the geometric figures or geometric shapes.

Circles, triangles, squares, rectangles, trapezoids, and parallelograms are some of the most memorable geometric figures. The area and perimeter of these solids are calculated using the following formulas,

• Square: Squares are four sides polygon and all the four sides are equal in length. All the four angles in the squares are equal to 90°. If the length of the side of a square is a, then,

• Area = a² square units,

• Perimeter = 4a units.

• Rectangle: Rectangle is also a four-sided polygon and the opposite sides are equal in length. Each angle in the rectangle is equal to 90°. If the length of the side of a rectangle is l, and the breadth of the rectangle is b, then,

• Area = l×b square units,

• Perimeter = 2 (l + b) units.

• Circle: Circle is a two-dimensional object drawn by a curve with same distance from the center. If the circle has a radius of r, then,

• Area = πr² square units,

• Perimeter = 2πr units.

• Triangle: Triangle is a three-sided polygon. If the height of the triangle is h, and the breadth of the rectangle is b,

• Area of triangle = (1/2) b×h square units,

• Perimeter of triangle = a + b + c units,

• where, a, b, c are side length of the triangle.

Among other geometric figures are:

• Acute Angle

An acute angle is less than a right angle, or less than 90 degrees.

• Arc

Any part of the circumference of a circle or other curve; a segment of a circle. The conic sections are the ellipse, parabola, and hyperbola.

• Cube

A regular, solid body with six equal square sides.

• Cylinder

A solid body supposed to be generated by the rotation of a parallelogram round one of its sides; or a long, circular body, of uniform diameter, and its extremities forming equal parallel circles.

• Diameter

A right line passing through the center of a circle, or other curvilinear figure, terminated by the curve, and dividing the figure symmetrically into two equal parts.

• Ellipse

In conic sections, a figure formed by the intersection of a plane and cone when the plane passes obliquely through the opposite sides of the cone.

• Hexagon

A plane figure of six sides and six angles. If the sides and angles are equal, it is a regular hexagon. The cells of honey-comb are hexagons, and it is remarkable that bees instinctively form their cells of this figure, which fills any given space without any interstice or loss of room.

1. Any part of the circumference of a circle or other curve is called diameter.

2. All the four angles in the squares are different.

3. Square is a two-dimensional object drawn by a curve with same distance from the center.

4. Hexagons are four sides polygon and all the four sides are equal in length.

5. Rectangle is a four-sided polygon and the opposite angles are equal in length.

6. A plane figure of six sides and six angles is called triangle.

7. Geometry is the mathematical study of shapes, figures, and liquids.

LANGUAGE DEVELOPMENT

4. Match up the words in column A with the words in column B to form meaningful phrases, translate them into Ukrainian:

Column A Column B

1. geometric a) section

2. regular b) body

3. conic c) angle

4. solid d) object

5. right e) figure

6. acute f) line

7. two-dimensional g) hexagon

5. Match the English words with their Ukrainian equivalents:

1. polygon a) коло

2. curve b) прямокутник

3. arc c) обертання

4. circumference d) трикутник

5. triangle e) дуга

6. rotation f) багатокутник

7. rectangle g) крива

6. Fill in the words from the list below. Use each word only once.

memorable, equal, study, sides, cone, polygon, length

1. ….. parallel circles

2. opposite sides of the …..

3. the most ….. geometric figures

4. the ….. of the side

5. mathematical ….. of shapes

6. four sides …..

7. a plane figure of six …..

7. Put these word combinations in the right order to make sentences:

1. Circle is / drawn by / same distance / a two-dimensional object / a curve with / from the center /.

2. Circles, triangles, and squares / or geometric shapes / rectangles, parallelogram / geometric figures / are some of the /.

3. Geometry is / of shapes, figures / and solids / the mathematical study/.

4. An acute angle / a right angle / 90 degrees / is less than / or less than/.

5. Squares are / and all / are equal / four sides polygon / the four sides / in length /.

6. Hexagon is / of six sides / a plane figure / and six angles /.

7. Cube is / square sides / with six equal / a regular, solid body /.