Simple closed figures

Task 1

Do you agree that "Without geometry, life is pointless"? If you do, have some fun:

What do you say when you see an empty parrot cage? – Polygon.

What is the best compliment to an equilateral triangle? – Nice legs!

Why is the obtuse angle so upset? – He is never right!

Task 2

Get ready for module text reading. Practice active vocabulary on the topic. First, read the words in the left column paying attention to their pronunciation. Then, find the Ukrainian equivalents in the right column. Spare column is left for your notes.

a simple closed figure in the space on the plane exact location a ray an angle to extend direction a common point the vertex of the angle interior, exterior right, acute, obtuse angle degree measure linear measure side boundary to enclose to intersect a polygon right, equilateral, isosceles triangle a leg and a hypotenuse opposite parallelogram quadrilateral trapezoidal a base of trapezoidal

прямий, гострий, тупий кути кордон, межа градусна міра міра сторін, їх довжина сторона внутрішній, зовнішній у просторі спільна точка на площині оточувати, вміщати перетинати проста замкнена фігура вершина кута точне розташування поширюватися промінь кут напрям трапеція основа трапеції протилежний прямокутний, рівносторонній, рівнобедрений трикутник катет та гіпотенуза чотирикутник багатокутник паралелограм прямокутник

Task 3

Read the text and underline the names of simple closed figures.

Simple closed figures

Geometry studies figures in the space and on the plane. The main geometric notions are the notions of a point and a line. A point is an exact location in space. A line consists of sets of points. Lines form line segments, rays and angles. A line segment includes endpoints and all points between them. A ray is a line segment extended in one direction.

Drawing two rays originating from the same endpoint we get an angle. The common point of the two rays is the vertex of the angle. Angles separate the plane into three distinct sets of points: interior, exterior, and the angle. The letter naming the vertex of an angle is the middle letter in naming of each angle.

A right angle has a measure of 90°. An acute angle has a degree measure less than 90°. An obtuse angle has a degree measure greater than 90°.

A simple closed figure is any figure drawn in a plane in such a way that boundary never crosses or intersects itself and encloses part of the plane. Every simple closed figure separates the plane into three distinct sets of point. The interior of the figure is the sets of all points in the part of the plane enclosed by the figure. The exterior of the figure is the set of point in the plane which are outside the figure. And finally, the simple closed figure itself is still another set of points.

A simple closed figure formed by line segments is called a polygon. Each of the line segments is called a side of the polygon. Polygons may be classified according to the measures of the angles or the measure of the sides. Triangle can be equilateral. The sides of such triangle all have the same linear measure. An isosceles triangle has two sides of the same measure. A right triangle has one right angle. A right triangle has two legs and a hypotenuse. A hypotenuse is a side opposite to the right angle.

A parallelogram is a quadrilateral whose opposite sides are parallel. So the set of all parallelograms is a subset of all quadrilaterals. A trapezoidal has only two parallel sides. They are called the bases of a trapezoidal.

Task 4

Draw simple figures. Let your partner check the drawings.

A parallelogram	A quadrilateral	A polygon
A line segment	An isosceles triangle	A square
A trapezoidal	A ray	A right triangle
An equilateral triangle	An obtuse angle	An acute angle

Task5

Read the text again and find the answers to the following questions:

1. What does geometry study?

2. What are the main geometric notions?

3. What is a point?

4. What does a line consist of?

5. What does a line form?

6. What does a line segment include?

7. What is a ray?

8. How can we get an angle?

9. What do we call a vertex of the angle?

10. How does the angle separate the plane?

11. What is a polygon?

12. What does a polygon consist of?

13. How can polygons be classified?

14. What is a triangle?

15. What types of triangle do you know?

16. What triangle do we call an equilateral one?

17. What is an isosceles triangle?

18. How do we call the sides of the right triangle?

19. What is a quadrilateral?

20. How do we call the sides of a trapezoidal?

Task 6

Fill in the gaps using the words from the box:

interior acute angle side polygon sets of points quadrilateral space

Exterior right crosses measure trapezoidal isosceles endpoints Lines Figures

intersects obtuse vertex of the angle equilateral opposite legs a line segment a point and a line

1. Geometry studies … in the space and on the plane.

2. The main geometric notions are the notions of … … .

3. A point is an exact location in ….

4. A line consists of … ….

5. … form line segments, rays and angles.

6. A line segment includes … and all points between them.

7. A ray is … extended in one direction.

8. Drawing two rays originating from the same endpoint we get an … .

9. The common point of the two rays is the ….

10. A right angle has a … of 90°.

11. An … angle has a degree measure less than 90°.

12. An … angle has a degree measure greater than 90°.

13. A simple closed figure is any figure drawn in a plane in such a way that boundary never … or … itself and encloses part of the plane.

14. The … of the figure is the sets of all points in the part of the plane enclosed by the figure.

15. The … of the figure is the set of point in the plane which are outside the figure.

16. A simple closed figure formed by line segments is called a ….

17. Each of the line segments is called a … of the polygon.

18. The sides of … triangle all have the same linear measure.

19. An … triangle has two sides of the same measure.

20. A … triangle has one right angle.

21. A right triangle has two … and a hypotenuse.

22. A hypotenuse is a side … to the right angle.

23. A parallelogram is a … whose opposite sides are parallel.

24. A … has only two parallel sides.

Task 7

Fill in the gaps: