Dimensional shapes

EXAMINATION

Spring semester 2012

Part 1. Geometry.

1. What are the sectors a circle can be divided into?

2. Which properties of a rectangular prism can be measured?

3. What is a triangle? What kinds of a triangle do you know? Tell about its properties.

4. What is a rectangle? Tell about its properties.

5. What is a square? Tell about its properties.

6. What is a circle? Tell about its properties.

7. What is a prism? Tell about its properties.

8. What is a pyramid? Tell about its properties.

9. What is a trapezoid? Tell about its properties.

10. What is a difference between a prism and a pyramid?

Part 2. Properties of materials.

1. What forms a compound?

2. How can some properties of elements change during a chemical reaction? Give an example.

3. How can some properties of elements not change during a chemical reaction? Give an example.

4. What is called “changes of state”? What do they depend on?

5. What are the different properties of a green branch (of a tree) and a dry branch?

6. What does it mean “transparent”, “translucent”, and “opaque”?

7. What are the properties of glass? Name at least five.

8. What are the properties of rubber? Name at least five.

9. What are the properties of wood? Name at least five.

10. What states of water do you know?

Part 3. Measurement.

1. How were measurements made in early times?

2. Why were early units only approximate? What did governments try to do?

3. How did a meter appear? How was it marked?

4. What is an English “foot-pound-second system”? Why did it loose ground against metric system?

5. What are the two systems of units used in the USA? What is the difference of their usage?

6. What units of measurement are used in cooking in Great Britain and the USA?

7. What is the difference between English and French distance measurement?

8. What ancient units of measurement do you know? What did they measure?

9. How was the metric system invented?

10. What ancient units of measurement are still used today? What do they measure?

D SHAPES

Triangle

A triangle is a figure formed when three noncollinear points are connected by segments.
Each pair of segments forms an angle of the triangle. The vertex of each angle is a vertex of the triangle.
The sum of the measures of the angles of a triangle is 180. The sum of the lengths of any two sides of a triangle must be greater than the third side. The subtraction of the lengths of any two sides of a triangle must be smaller than the third side.

Triangles can be classified by:

Their sides:

Equilateral- All three sides have equal lengths

Isosceles - Exactly two equal sides

Scalene- All sides have different lengths

Their angles:

Acute - All interior angles are acute (<90º)	Right - One angle is a right angle (90º)	Obtuse- One angle is obtuse (>90º)

Square

A square is a parallelogram with 4 congruent sides and 4 right angles.
A square is a particular case of a rectangle and a rhombus simultaneously. So, it shows both the properties of rhombus and rectangle simultaneously.
Square can be differentiated from a rectangle and rhombus due to following properties:

1. Unlike rectangle square needs to have all its sides equal.
2. Unlike rhombus square needs to have all angles equal to 90 degree.

Rectangle

A rectangle is a four-sided polygon with four right angles, whose opposite sides are parallel and are equal.
A rectangle is a particular sort of parallelogram, but can't say that all parallelograms would be rectangles, because a rectangle is a shape where opposites sides are parallel and all the corners are 90 degree angles. Some parallelograms would be rectangles, but not all.

Circle

A circle is a plane figure, bounded by a single curve line called its circumference, every part of which is equally distant from a point within it, called the center.
A circle sector is any piece of the circle between two radial lines (shaded in both dark and clear grey).
A segment of a circle is the region between a chord of a circle and its associated arc (shaded in dark grey).
An annulus is the region lying between two concentric circles

dimensional shapes

Circles

You already know that a circle has 360°. Circles can be divided into different sectors: a half circle or semi-circle has 180°, a quarter circle has 90°, and an eighth of a circle has 45°.

Triangles

A triangle is a closed figure that has three sides and three angles. The sum of the three angles of every triangle always equals 180°. A right triangle always has one angle equal to 90° and two angles whose sum is 90°, making a total of 180°.

Rectangles

A rectangle is a four sided shapewith four right angles(90°).The sides across from each other are always the same length and always parallel to each other.The four angles add up to a total of 360°.

Another important rule about rectangles is that the diagonals of a rectangle are equal.Diagonals are lines that run between opposite corners.A diagonal always divides a rectangle exactly in half and creates two equal right triangles.

Squares

The square is a special type of rectangle in which all sides are equal. Since the square is a rectangle, the same rules that apply to the rectangle also apply to the square. A diagonal across the square creates two equal45° right triangles. It will be helpful to remember thatthe 45° right triangle ishalf of a square.

Rhombus

A rhombus is actually just a special type of parallelogram. Recall that in a parallelogram each pair of opposite sides are equal in length. With a rhombus, all four sides are the same length. It therefore has all the properties of a parallelogram.

It’s a bit like a square that can 'lean over' and the interior angles need not be 90°. Sometimes called a 'diamond' or 'lozenge' shape.

Trapezoid

A trapezoid is a 4-sided figure with one pair of parallel sides. Every trapezoid has two bases. Each base of a trapezoid must be perpendicular to the height. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2.

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