Lekcja 5. Geometric shapes

07 stycznia 2016

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Figury geometryczne po angielsku

A geometric shape is the geometric information which remains when location, scale, orientation, and reflection are removed from the description of a geometric object. That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original.

Objects that have the same shape as each other are said to be similar. If they also have the same scale as each other, they are said to be congruent. If a shape contains all the line segments connecting any pair of its points, it’s called a convex polygon. In convex polygons no angle has a measure greater than 180 degrees.

Geometric shapes defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points are called polygons and include triangles, squares, and pentagons. Some shapes may be bounded by curves, e.g. the circle and the ellipse.

2-dimensional geometric shapes

	A circle is the set of all points on a plane that are at a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure or to the whole figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk. The picture shows a circle with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre (O) in magenta.
	An ellipse is a curve on a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
	An equilateral triangle is a triangle in which all three sides are equal and all three internal angles are also congruent to each other and are each 60°.
	An isosceles triangle is a triangle that has two sides of equal length.
	A parallelogram is a quadrilateral that has two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
	A pentagon is any five-sided polygon.
	A rectangle is any quadrilateral with four right angles. It can also be defined as a parallelogram containing a right angle.
	A rhombus, plural rhombi or rhombuses, is a simple quadrilateral with all four sides of the same length. The rhombus is often called a diamond. Every rhombus is a parallelogram. The height h is the perpendicular distance between any two non-adjacent sides or the diameter of the circle inscribed.
	A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles or right angles).
	A trapezoid (US and Canada), trapezium (UK and anywhere else) is a convex quadrilateral with at least one pair of parallel sides.

Vocabulary

Exercises

Exercise 1. Match the words in column A with the ones in column B.

Exercise 2. Answer the following questions.

1. What is a geometric shape?
2. What geometric objects are similar?
3. What geometric objects are congruent?
4. What is a polygon?
5. What is a convex polygon?
6. What is a circle?
7. What is the difference between the terms „circle” and „disk”?
8. What is an ellipse?
9. What is an equilateral triangle?
10. What is an isosceles triangle?
11. What is a parallelogram?
12. What is a pentagon?
13. What is a rectangle?
14. What is a rhombus?
15. What is another often used name for a rhombus?
16. What is a square?
17. What is a trapezoid?

Exercise 3. Write sentences with the expression "the former and the latter" as in the example. In most cases there are many possible answers.

rhombus and pentagon -> The former is a quadrilateral and the latter is a five-sided polygon.

1. trapezoid and octagon (eight sides)
2. square and hexagon (six sides)
3. rhombus and disk
4. rectangle and triangle
5. pentagon and quadrilateral
6. parallelogram and circle
7. isosceles triangle and square
8. equilateral triangle and octagon
9. ellipse and circle
10. circle and disk

Exercise 4. Przyjrzyj się poniższemu bardzo niezwykłemu wierszowi i spróbuj odgadnąć na czym polega jego niezwykłość. Nie doszukuj się ukrytych znaczeń ani nie wczytuj się zbytnio w samo znaczenie słów.

I often wondered when I cursed,

Often feared where I would be —

Wondered where she'd yield her love,

When I yield, so will she.

I would her will be pitied!

Cursed be love! She pitied me…

Exercise 5. Translate the Polish part of the following sentences into English.

The result of… (W wyniku…)

1. przesunięcia trójkąta równobocznego kształt figury się nie zmieni.
2. powiększenia trójkąta równoramiennego kształt figury się nie zmieni.
3. rotacji kwadratu kształt figury się nie zmieni.
4. odbicia w lustrze równoległoboku kształt figury się nie zmieni.
5. przesunięcia prostokąta kształt figury się nie zmieni.
6. powiększenia trapezu kształt figury się nie zmieni.
7. rotacji kwadratu kształt figury się nie zmieni.
8. odbicia w lustrze koła kształt figury się nie zmieni.
9. rotacji elipsy kształt figury się nie zmieni.

Exercise 6. True or false?

1. Every square is a rectangle.
2. Every rectangle is a square.
3. Every square is a rhombus.
4. Every rhombus is a square.
5. Every rectangle is a parallelogram.
6. Every parallelogram is a rectangle.
7. Every rhombus is a parallelogram.
8. Every parallelogram is a rhombus.
9. Every parallelogram is a quadrilateral.
10. Every quadrilateral is a parallelogram.
11. Every circle is an ellipse.
12. Every ellipse is a circle.

Exercise 7. Write sentences using the information from the previous exercise as shown in the example.

Every circle is an ellipse, but not every ellipse is a circle.

Exercise 8. Change the above sentences into plural form following the example. Write down your sentences.

All squares are rectangles, but not all rectangles are squares.

Exercise 9. Repeat exercises 7 and 8 orally. Don’t look at the sentences you have written previously.

Exercise 10. Translate the following texts into English.

1. Równoległobok to wielokąt mający dwie pary boków równoległych. Przeciwległe boki równoległoboku są tej samej długości, a przeciwległe kąty równoległoboku mają tę samą miarę.
2. Trójkąt to figura geometryczna mająca trzy boki. Dwa lub trzy z boków trójkąta mogą być tej samej długości, podobnie jak dwa lub trzy kąty trójkąta mogą być tej samej miary.
3. Pięciokąt to wielokąt mający pięć boków. Boki mogą być różnej długości, a kąty wewnętrzne mogą mieć różną miarę.
4. Prostokąt to wielokąt mający dwie pary boków równoległych i cztery kąty proste. Przeciwległe boki wielokąta mają jednakową długość. Każdy prostokąt jest także równoległobokiem.
5. Romb to równoległobok o wszystkich bokach równych. Przeciwległe kąty równoległoboku mają tę samą miarę.
6. Trapez to wielokąt wypukły mający przynajmniej jedną parę boków równoległych. Trapez z dwiema parami boków równoległych jest równoległobokiem.

Exercise 11. Look at the pictures and describe them orally as in the example.

These two objects have the same shape as each other, so they are similar. They are triangles.

Exercise 12. Look at the geometric shapes in exercise 9 and say sentences about each of them as shown in the example.

A triangle is a three-sided, 2-dimensional geometric shape.

Exercise 13. Play the video from the beginning of the lesson again, turn on English subtitles and speak together with the speaker. Repeat the exercise as many times as is necessary to speak fluently.

Exercise 14. Watch the following video and answer the questions below.

1. What is the subject of the video?
2. What ways of categorizing triangles does the author mention?
3. What is a scalene triangle?
4. What is an isosceles triangle?
5. What is an equilateral triangle?
6. Are all equilateral triangles also isosceles triangles?
7. What is an acute triangle?
8. What is a right triangle?
9. What is an obtuse triangle?
10. How is the right angle marked in a right triangle?
11. Is it possible to have a right scalene triangle?
12. Are all equilateral triangles right, obtuse or acute?

Exercise 15. Play the video from exercise 14 again, turn on English subtitles and speak together with the speaker. Repeat the exercise as many times as is necessary to speak fluently.

Exercise 16. Translate the text into Polish.

Exercise 17. Summarize the text orally using questions from exercise 2 as an outline. Practice until you can say the summary without looking at the text.