1. Basic geometric figures
- Points on a line are called "colinear", on a plane "coplanar"
- A geometric figure is a set of points
- Geometric figures - plane or space
a point - defined by a dot and denoted by a capital letter
a line - extends infinitely, denoted by a small letter
a plane - extends infinitely in all directions, denoted by a Greek letter
a ray - has an endpoint, but extends infinitely
a segment - consists of 2 endpoints and all points that lie between
2. Angles
- An angle is formed by two rays with a common endpoint
vertex - the cornet point of an angle
arms - two straight sides (rays)
interior angle - angle inside the shape
exterior angle - angle between side of the shape, a line extended from the next side
miara kąta - measure of an angle
dwusieczna kąta - bisector
kąt odpowiadający - corresponding angle
Types of angles:
- zero angle (0)
- acute (0-90)
- right (90)
- obtuse (90-180)
- straight (180)
- reflex (180-360)
- round angle (360)
Types of pairs of angles:
- congruent (the same measure)
- vertical (formed by 2 intersecting lines, have the same measure)
- adjacent (have common vertex, common side and no common interior points)
- complementary (sum of their measures is 90; a + b = 90)
- supplementary (sum of their measure is 180)
horizontally - poziomo
diagonally - ukośnie
vertically - pionowo
3. Triangles
- A triangle is a polygon, that has three sides/three angles
polygon - wielokąt
- The sum of measures of a triangle's interior angles is equal to 180
Types of angles:
By angles:
acute-angled triangle - ostrokątny
obtuse-angled triangle - rozwartokątny
right-angled triangle - prostokątny
By sides:
equilateral (all sides have the same length) - równoboczny
isoceles (at least 2 sides have the same length) - równoramienny
scalener (length of sides are different) - różnoboczny
hypotenuse - przeciwprostokątna
legs - przyprostokątne
diagonal - przekątna
perpendicular - prostopadły
parallel - równoległy
4. Quadrilaterals
- Any four-sided polygon is called a quadrilateral
Classification:
Quadrilaterals - trapezoids, kites, other quadrilaterals
Trapezoids - parallelograms, other trapezoids
Parallelograms - rectangles, rhombus, squares
a trapezoid - has at least 1 pair of parallel sides
a parallelogram - hast 2 pairs of parallel sides
a square - all sides are equal, all angles are right, both pairs of sides are parallel
a rhombus - has 2 pairs of parallell sides, all sides are equal
a perimeter - obwód
a parallelogram - równoległobok
a rectangle - prostokąt
a square - kwadrat
a rhombus - romb
5. Circles
- A circle is a set of points on a plane, that are the same distance from a fixed point (this given distance is called "radius")
circumference (L) - obwód okręgu
a circle - okrąg
a disc - koło
secant - sieczna
chord - cięciwa
tangent - styczna
diameter - średnica
radius - promień
area (A) - pole powierzchni
a radius (plural: radii) - a segment which joins the centre of a circle and the point on a circle
a chord - a segment joining two points on a circle
a diameter - a chord, that contains a center - the longest chord is diameter
Types of pairs of circle:
A circle & a line:
- Points on a line are called "colinear", on a plane "coplanar"
- A geometric figure is a set of points
- Geometric figures - plane or space
a point - defined by a dot and denoted by a capital letter
a line - extends infinitely, denoted by a small letter
a plane - extends infinitely in all directions, denoted by a Greek letter
a ray - has an endpoint, but extends infinitely
a segment - consists of 2 endpoints and all points that lie between
2. Angles
- An angle is formed by two rays with a common endpoint
vertex - the cornet point of an angle
arms - two straight sides (rays)
interior angle - angle inside the shape
exterior angle - angle between side of the shape, a line extended from the next side
miara kąta - measure of an angle
dwusieczna kąta - bisector
kąt odpowiadający - corresponding angle
Types of angles:
- zero angle (0)
- acute (0-90)
- right (90)
- obtuse (90-180)
- straight (180)
- reflex (180-360)
- round angle (360)
Types of pairs of angles:
- congruent (the same measure)
- vertical (formed by 2 intersecting lines, have the same measure)
- adjacent (have common vertex, common side and no common interior points)
- complementary (sum of their measures is 90; a + b = 90)
- supplementary (sum of their measure is 180)
horizontally - poziomo
diagonally - ukośnie
vertically - pionowo
3. Triangles
- A triangle is a polygon, that has three sides/three angles
polygon - wielokąt
- The sum of measures of a triangle's interior angles is equal to 180
Types of angles:
By angles:
acute-angled triangle - ostrokątny
obtuse-angled triangle - rozwartokątny
right-angled triangle - prostokątny
By sides:
equilateral (all sides have the same length) - równoboczny
isoceles (at least 2 sides have the same length) - równoramienny
scalener (length of sides are different) - różnoboczny
hypotenuse - przeciwprostokątna
legs - przyprostokątne
diagonal - przekątna
perpendicular - prostopadły
parallel - równoległy
4. Quadrilaterals
- Any four-sided polygon is called a quadrilateral
Classification:
Quadrilaterals - trapezoids, kites, other quadrilaterals
Trapezoids - parallelograms, other trapezoids
Parallelograms - rectangles, rhombus, squares
a trapezoid - has at least 1 pair of parallel sides
a parallelogram - hast 2 pairs of parallel sides
a square - all sides are equal, all angles are right, both pairs of sides are parallel
a rhombus - has 2 pairs of parallell sides, all sides are equal
a perimeter - obwód
a parallelogram - równoległobok
a rectangle - prostokąt
a square - kwadrat
a rhombus - romb
5. Circles
- A circle is a set of points on a plane, that are the same distance from a fixed point (this given distance is called "radius")
circumference (L) - obwód okręgu
a circle - okrąg
a disc - koło
secant - sieczna
chord - cięciwa
tangent - styczna
diameter - średnica
radius - promień
area (A) - pole powierzchni
a radius (plural: radii) - a segment which joins the centre of a circle and the point on a circle
a chord - a segment joining two points on a circle
a diameter - a chord, that contains a center - the longest chord is diameter
Types of pairs of circle:
A circle & a line:
©2011-2013 by Oskar Zmarzły