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5th Grade - Geometry

5th Grade lesson

5 - Geometry


Parallel lines, perpendicular lines

Two straight lines are parallel if they never intersect.
Two straight lines are perpendicular if they form a right angle, that is, an angle that measures 90 degrees.
The yellow lines are parallel
parralel lines
The green lines are perpendicular
perpendicular lines


Perimeter, area

The perimeter of a figure is the length of the circumference of the figure, the area of a figure is its surface, that is the number of small squares of edge 1 that we can put inside.
area and perimeter
The rectangle below has a perimeter measuring 3 + 4 + 3 + 4 = 14 cm, and an area of 12 cm².


Triangles

A triangle is a figure which has 3 edges. There are several types of triangles :

A triangle which has 3 edges of the same length is called an equilateral triangle.
A triangle which has 2 edges of the same length is called an isosceles triangle.
A triangle which has a right angle is called a right-angled triangle.

The height of a triangle (red line) is the straight line which passes through a vertex and which is perpendicular to the opposite edge, called the base (green line).
The area of a triangle is equal to the length of the base (in green) times the length of the height (in red), divided by 2.

equilateral triangle
The triangle above is an equilateral triangle.
isosceles triangle
The triangle above is an isosceles triangle.
rectangular triangle
The triangle above is a right-angled triangle.

The area of each of the three triangles above is equal to the length of the green edge times the length of the red segment divided by two.



Quadrilaterals

A quadrilateral is a figure which possesses 4 edges.

The diagonals in a quadrilateral are the straight lines which join opposite vertices.

A quadrilateral whose opposite edges are parallel is called a parallelogram. Its diagonals intersect at their centre. Conversely, if the diagonals of a quadrilateral intersect at their centre, then that quadrilateral is a parallelogram.

Parallelogram :
parallelogram

A quadrilateral which has 4 right angles is called a rectangle. Its diagonals intersect at their centre and have same length.

Rectangle :
rectangle

A quadrilateral which has 4 right angles and 4 edges of the same length is called a square. Its diagonals intersect at their centre, have same length, and are perpendicular.

Square :
square

If the diagonals are perpendicular but do not have the same length, then the quadrilateral is a diamond. It is a quadrilateral which has 4 edges of the same length.

Diamond :
diamond


Circle

The number pi is approximately 3,14.
The perimeter of a circle of radius r is equal to circle perimeter.
The area of a circle of radius r is equal to circle area.
circle



See also : geometry on fmaths.com



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5th Grade Geometry

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