Transcript Geometry

Geometry
Quadrangle
- Shape, which has 4 sides and 4 angle.
- The sum of the measures of the interior angles of any quadrangle is 360 °.
Thrapezium
- Thrapezium has at least a pair of parallel sides.
- Sum of thrapezium’s angles, lying at the same arm is equal to 180o.
- Formula to calculate the area:
P
( a  b)  h
2
P - area
a - lenght of higher base
b - lenght of lower base
h - height
- An isosceles thrapezium’s diagonals intersect at right angles.
Parallelogram
- Parallelogram is a thrapezium.
- It has 2 pair of parallel sides.
- His parallel sides have the same length.
- His diagonal intersect in half of their length.
- Formula to calculate the area:
P  ah
P - area
a - lenght of base
h - height
Rhomboid
- Rhomboid has 2 pair sides of the same lenght.
- Sides of the same length are in contact with.
- Angles between sides of different length are the same.
- Formula to calculate the area:
e f
P
2
P - area
e - first diagonal
f - second diagonal
Rhombus
- The sum of two adjacent angles is equal to 180o.
- The diagonals intersect at an right angle and divide
rhombus into four right-angled triangles.
- His sides are the same.
- Formula to calculate the area:
P  e f
P - area
e - first diagonal
f - second diagonal
Rectangle
- Rectangle has 2 pair sides of the same lenght.
- His diagonals are the same.
- All angles of rectangle have 90o.
- Rectangle has 2 pairs of parallel sides.
- Formula to calculate the area:
P  a b
P - area
a - first side
b - second side
Square
-All angles are right.
-All sides are the same.
-His diagonal intersect at right angles.
-His diagonals are the same.
- Formula to calculate the area:
Pa
2
Formula to calculate the diagonal:
d a 2
P – area
a – side
d - diagonal
Triangle
- Triangle has 3 sides.
- Sum of his angles is equal to 180o.
Types:
Classification by the sides:
- a scalene triangle – all his sides have different length.
- an isosceles triangle – both arms have the same length.
- an equilateral triangle – all his sides have the same lenght.
Classification by the angles:
- an acute-angled triangle – has 3 acute angles.
- an right-angled triangle – has 1 right angle and 2 acute angles.
- an obtuse-angled triangle – has 1 obtuse angle and 2 acute angles.
Formula to calculate the area:
ah
P
2
P - area
a - base
h - height
Equilateral triangle
- All sides have the same lenght.
- All angles are equal to 60o.
- Formula to calculate the area:
P
a
2
3
4
- Formula to calculate the height:
a 3
h
2
P - area
a - side
h - height