English Mathematics UHAMKA

8/10/2019 English Mathematics UHAMKA

1/38

English For Mathematics


2/38

The PERPENDICULAR distance from the

BASE of a figure to the opposite VERTEX. The

altitude is also called the height. A triangle

has three altitudes. Any side can be

considered the base.


3/38

Examples:

h is the altitude.

Practice: Draw the

altitude to the side

marked b.1)

h

vertex

2) vertex

h

b


4/38

The amount of surface inside a plane figure.

Area is measured in square units.

The formulas is:

RECTANGLE : Area A = lw,

Where l= length

And w= width.w

l


5/38


6/38


7/38

Geometric figures where any line segment connecting two points is inside the

figure. Compare CONCAVE.

Examples:


8/38

Definition: A system in which graphs with geometric figures are represented by equations.

(It is also called analytic geometry.)

Example :

1. The graph of the equationy =x + 2 is a straight line:

PointA has the COORDINATES (1,3) and satisfies the

equation, i.e. 3 = 1 + 2. Point B has the coordinates (0,2)

and satisfies the equation, i.e. 2 = 0 + 2.

2. An equation inx and y has a straight line as a graph when the exponents

of bothx andy equal 1 (and are therefore not written out). When the

exponent of either x ory (or both) is equal to 2 or more, the graph is a

curve.

The graph of the equation y =x2 is a curve (parabola):

PointA has the coordinates (-2,4) and satisfies the equation, i.e. 4 = (-2)2.

Point B has the coordinates (-1,l) and satisfies the equation, i.e. 1 = (-1)2.

Point C has the coordinates (0,O) and satisfies the equation, i.e. 0 = 02.

Point D has the coordinates (1,l) and satisfies the equation, i.e. 1 = 12.

Point E has the coordinates (2,4) and satisfies the equation, i.e. 4 = (2)2.


9/38

Example:

.... Is the diagonal

Definition: The distance across a CIRCLE through its center. The diameter

is twice the RADIUS. All of the straight dotted lines in the

figure are diameters.


10/38

A line segment that separates the FACES of a solid figure.

Example:

EDGE

A cube has 12 edges.


11/38

A triangle with equal sides. All angles are 60.

Example: If the PERIMETER of an equilateral triangle is 30

cm, all sides are 10 cm. (30+3=10)


12/38

.


13/38

The largest side in a right (90") triangle. It is across

from the right angle. See also the PYTHAGOREAN THEOREM.

Example:

c

Slide c is the hypotenuse


14/38

ANGLE: An angle inside acircle with itsVERTEX on thecircle. Its sides are

CHORDS.

FIGURE: A polygon insidea circle with all itsVERTICES onthecircle.


15/38

The inside of a geometric figure.

Example:

Interior


16/38

A triangle with two equal sides.

In triangle ABC, the sides a and b are equal. The angles A

and B are also equal.

Example:

ab

cA B

C


17/38

The total distance along a line. The basic unit of length in the

METRIC SYSTEM is the meter. One meter is a little longer a yard.

Example:

1,5 cm

3 cm

The length is 3 cm.


18/38

An infinite collection of points. A line has direction but

neither a beginning nor an end.

Example :

1) Line 2) A Horizontal Line


19/38

Part of a line with a beginning and an end.

Symbol: - (a bar above the points defining the beginning and end

of the line segment)

Example :

is a line segment. is a line.

A B

ABis the length of the line segment.


20/38

Apoint that divides a LINE SEGMENT into two

equal parts.

Example :

A B C

B is the midpount betweenA and C ,

provided thatAB = BC.


21/38

Definition: The distance round the edge of a plane figure.

The perimeter1 P = l + w + I + w =21+2w.

In

l

w

Example:

The perimeter of a circle is called the circumference.


22/38

The distance from the center of a circle to any point on

its circumference. The plural of radius is radius.

Example :

r


23/38

Of a line:

A piece of a straight line with

a beginning and an end.

Of a circle:

A part of a circle that is

bordered by a chord and the

arc, which is formed by thechord.


24/38

Semicircle is a half-circle.


25/38

Geometric figures with the same shape

but with different size.

Example :


26/38

The ratio between corresponding sides in similar

figures.

Example:


27/38

A line that touches a curve at one point. Tangent

also means the ratio of the legs of a right triangle.

Examples:


28/38

TRAPEZOID

A four-sided figure with one

set of parallel sides.

TRIANGLE

A three-sided figure.


29/38

The extent of space occupied by a solid, a liquid or a gas. Volume

of a solid is measured in cubic length units. Volume of a liquid or a gas is

measured in cubic liquid units. See the METRIC SYSTEM.

Example :

1. The volume of a box is measured aslength x width x height.

2. The volume of a bottle of water is measured in liters.

3. The volume of a propane tank is measured in gallons


30/38

The force by which an object is attracted by the

Earth. Mass and weight are used interchangeably in

everyday 1anguage.

Example:

The weight of a

person

is measured on a

scale

in units of pounds

or kilograms.


31/38

A LINE SEGMENT (part of a straight line) that joins

two points on a curve.

Example:


32/38

A geometric figure that is drawn exactly aroundanother geometric figure. The figures involved are usually

one circle and one POLYGON, such as a triangle or a square.

Com- pare with INSCRIBED.

Example:


33/38

Parts of geometric figures that have the sameposition within each figure.

Symbol:

Example:


34/38

In geometry:Definition: A solid (three-dimensional) figure with six square FACES.

Examples:

1.

The volume of a cube with a 2-cm side is (2 ~m)~ = Z3 cm3 = 8 cm3

2.

Each face of the cube in Example 1 has an area of 22 cm2 = 4cm2.


35/38

VERTICAL

ANGLESAngles that are opposite of

each other when two lines

intersect.

VERTICAL

LINESLines that arePERPENDICULAR (at right

angle) to the horizon or the

ground. The equation of a

vertical line is x = a,where ais a real number (usually an

integer).


36/38

HEPTAGON

A POLYGON (many-sidedplane figure) with seven

sides.

Example:

HEXAGON

A POLYGON (many-sidedplane figure) with six sides. All

sides of a regular hexagon are

equal.

Example :


37/38

A image of a figure. See

also AXIS

A point that is common to two

lines in an angle or a polygon.

The plural form of vertex is

vertices. An angle has one

vertex, a triangle has three

vertices and a square has four

vertices.


38/38

Documents

English Mathematics UHAMKA