Kori on tyhjä
Geometry
Look at the objects in the image above. Write one property of each.
The word geometry comes from the Greek 'geo', meaning earth, and 'metron', meaning measurement. Geometry is one of the oldest branches of mathematics and its scientific foundations were laid by ancient Greek mathematicians.
Two Hungarian mathematicians, Farkas Bolyai \latex{ (1775-1856) } and his son, János Bolyai \latex{ (1802- 1860) }, are known for their great achievements in the field of geometry. You will learn more about their work later.
Geometry is the study of, among other things, the size and shape of objects. In geometry, objects are drawn in a simplified way, showing only the properties that are of geometrical interest. To discuss these, it is necessary to use expressions that mean the same thing to everyone.
The book, the ruler, the orange, the clock, the globe ..... are solids.
Solid objects are bounded by surfaces, which can be either flat or curved.
Solid objects are bounded by surfaces, which can be either flat or curved.
The surfaces of flat shapes are bounded by lines, which can be straight or curved.
\latex{ b }
\latex{ c }
Lines are denoted by lowercase letters of the alphabet.
When two lines intersect, they create a point. Points are denoted by the capital letters of the alphabet.
Solid objects, surfaces, lines and points are all made up of a set of points called loci.
Solid objects, surfaces, lines and points are all made up of a set of points called loci.
Wherever you are, you are surrounded by various objects. Some of them are smaller, larger, similar, the same or different in shape.
\latex{ e }
\latex{ P }
\latex{ f }
their size and shape are the
same
same
their shape is the same, but
their size is different
their size is different
their shape is different
congruent solids
incongruent solids
Points are marked by:
\latex{ A }, \latex{ B }, \latex{ C }, ..., \latex{ P }, ...
On a figure:
\latex{ A }, \latex{ B }, \latex{ C }, ..., \latex{ P }, ...
On a figure:
\latex{ A }
\latex{ B }
their size and shape are the
same
same
their size is different
their shapes are different
congruent flat shapes
incongruent flat shapes
Exercises
{{exercise_number}}. What type of surfaces border the following objects?
a) a blackboard
b) a piano
c) a bench
d) a rubber mat
{{exercise_number}}. Make a list of solids that have...
a) only plane surfaces;
b) only curved surfaces;
c) both plane and curved surfaces.
{{exercise_number}}. What kind of lines bound the surface of the following objects?
a) ruler
b) pencil case
c) book
d) your hand
{{exercise_number}}. What kinds of surfaces and lines can you find on a matchbox?
{{exercise_number}}. What kinds of surfaces and lines are there on a rectangular block?
{{exercise_number}}. The image below shows the letters used in technical drawings. Which letters of the alphabet are drawn only with straight lines and only with curved lines?
\latex{N}
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ H }
\latex{ I }
\latex{ J }
\latex{ K}
\latex{ L}
\latex{ M}
\latex{ Z}
\latex{ Y}
\latex{ X}
\latex{ W}
\latex{ V}
\latex{ U}
\latex{ T}
\latex{ S}
\latex{ R}
\latex{ Q}
\latex{ P}
\latex{O}
{{exercise_number}}. Are the two figures in the images congruent?
a)
b)
c)
d)
{{exercise_number}}. Are the two stamps congruent?
a)
b)
c)
d)
{{exercise_number}}.
a) What characterises the solids in set \latex{ A }?
b) What characterises the solids in set \latex{ B }?
c) What is common to the solids in the intersection of the sets?
b) What characterises the solids in set \latex{ B }?
c) What is common to the solids in the intersection of the sets?
A
B
{{exercise_number}}. Look for congruent and incongruent pieces in a chess set.
Quiz
Find the differences between the two pictures.
