Geometry Flashcards
What is a straight line?
A straight line is the shortest distance between two points or a set of points
with no definite starting-point or end point.
What is a line segment?
A line segment is a set of points with a definite starting point and end point.
What is a ray?
A ray is a set of points with a definite starting point and no definite end point.
Two intersecting straight lines are said to be perpendicular when the angle
they form is ……
equal to 90º.
We use a little square to indicate when an angle is a ….
right angle (equal to 90º).
When two line segments are _______________, we indicate this with the ┴
symbol.
perpendicular
We say two straight lines are ________________ when the perpendicular distance
between the two lines is constant.
parallel
we indicate lines that are _____________ with little arrows on the lines.
parallel
When two line segments AB and CD are __________________ , we use the symbol ║to
indicate this.
parallel
A line consists of an uncountable number of points in a __________________ and it has
_______________
straight line
length
A ______________________ is any part of a line. It has a beginning and an end, which is
indicated by capital letters.
Line segment
A ray has a definite beginning but _________________.
A ray can be found in an angle
No end
Parallel lines are lines that are the same _________________
and extend in the __________________ .
distance apart
same direction
Do parallel lines intersect?
Never
what is a vertical line
A straight line going from the top to the bottom or bottom to top
What is a horizontol line
A straight line that goes from left to right or right to left
What are diagonal lines
Straight lines that are slanted
What is an angle?
An angle is formed when two rays start from the same point of origin, but rotate away from each other.
What is the magnitude of the angle?
The magnitude or size of the angle is therefore the measurement that shows how far one of the rays has rotated.
What measurement are angles measured in?
What do we use to measure angles?
Angles are measured in degrees.
We use a protractor to measure the size of the angle
Name and describe the different types of angles
Acute angle - is smaller than 90 Deg
Right Angle - is 90 Deg
Obtuse Angle - is bigger than 90 Deg
Straight Angle - is 180 Deg
Reflex Angle - between 180 and 359 Deg
Revolution - 360 Deg
Where are angles formed?
Angles are formed wherever two straight lines or edges meet.
The straight lines or edges that form the angle are called …..
the arms
The point where the arms of an angle meet are called …..
the vertex.
The plural of vertex is ……
vertices
You can indicate an angle by drawing __________ between its arms
an arc
How does one measure a reflex angle?
By measuring the acute angle opposite the reflex angle and subtracting it from 360 Deg
What are polygons?
Polygons are shapes that have 3 or more sides
What is a regular polygon?
This means that the sides and angles of the polygon are equal in size.
What is an irregular polygon?
This means that the sides and angles of the polygon are not the same size.
How are polygons classified?
according to the number of sides and angles that they have.
A polygon with 3 sides
Triangle
A polygon with 4 sides
Quadrilateral
A polygon with 5 sides
Pentagon
A polygon with 6 sides
Hexagon
A polygon with 7 sides
Heptagon
A polygon with 8 sides
Octagon
A polygon with 9 sides
Nonagon
A polygon with 10 sides
Decagon
What are the properties of a triangle?
A triangle is a shape that has 3 sides and 3 angles.
The interior angles of a triangle always adds up to 180 deg
Equilateral triangles:
All 3 sides are equal
Isosceles triangle:
Two of the sides are equal
Scalene triangle:
None of the sides are equal
Acute-angled triangle:
All 3 angles are acute (i.e. less than 90 deg)
Obtuse-angled triangle:
One of the angles is an obtuse angle (i.e. bigger than 90deg)
Right-angled triangle:
One of the angles is a right angle (i.e. 90deg)
How do you need to name triangles?
You need to name triangles according to their
sides and angles. (Right-angled isosceles triangle)
A line that forms the circle.
Circumference
A line that passes through the centre of the circle and joins two points on the circumference.
Diameter
Any straight line drawn from the centre of the circle to any point on the circumference.
Radius
A point in the middle of the circle that is an equal distance from every point on the circumference
Centre
Part of the circumference of the circle
Arc
calculate the area of a rectangle with sides 3.7cm and 5cm
Area = 3.7cm x 5cm
= 37mm x 50mm
= 37 x 100 / 2
= 370 / 2
= 185mm
= 18.5cm (squared)
calculate the area of a L-shaped room.
6m x 9m x 3m x 7m x A x B
A = 3m and B = 2m
Divide the room into 2 rectangles.
Area = (7m x 3m) + (6m x 2m)
= 21m + 12m
= 33m (sq)
Calculate the area of a right-angles triangle that is 6mm x 6mm x 90cm
Area = (6mm x 6mm) / 2
= 36mm / 2
= 18mm (sq)
= 1.8cm (sq)
The area of a square is 49cm(sq)
What is the length of one side of the square?
What are the factors of 49?
1, 49, 7
=7cm
The perimeter of a hexagon.
2 sides are 22.6m and 4 sides are 15.5m
Perimeter = 22.6m x 2 + 15.5m x 4
= 44 + 1.2 + 60 + 2
= 107.2m
What is a scalene triangle?
No sides are equal
What is an equilateral triangle?
All Sides are equal
What is an isoceles triangle
2 sides are equal
What is a right angles triangle
One Angle in side the triangle is a right angle
What is an obtuse triangle?
One angle in a triangle is obtuse
What is an acute angle?
All angles in the triangle are acute angles.
In a quadrilateral, calculate x
^ A = 65 Deg
^ B = 85 Deg
^ C = 127 Deg
^ D = ?
All angles inside a quadrilateral add up to 360 Deg
= 360 - (65 + 85 + 127)
= 360 - (150 + 127)
= 360 - 277
= 83
D = 83 Deg
Calculate the perimeter of a rectangle with length of 12cm
and a width of 30mm
Perimeter = L x 2 + B x 2
= 12cm x 2 + 30mm x 2
= 24cm + 60mm
= 24cm + 6cm
= 30cm
Calculate the area of a rectangle with length of 12cm
and a width of 30mm
Area = L x W
= 12cm x 3cm
= 36cm (sq)
Right- angled Triangle with Sides
7.2cm x 6.5cm x 12.3cm
Area = L x H /2
= 7.2 x 6.5 / 2
= (7.2 x 6 + 7.2 x 0.5) / 2
= (42 + 1.2 + 3.5 + 0.1) / 2
= 46.8 / 2
= 23.4cm (sq)
Calculate the Surface area of a rectangular prism with measurements:
10cm (l) x 3cm (w) x 5cm (h)
Surface Area: 2(L x h + L x B + B x H)
= 2(10cm x 5cm + 10cm x 3cm + 3cm x 5cm)
= 2(50cm(sq) + 30cm(sq) + 15cm(sq))
= 2 x 95cm(sq)
= 190cm (sq)
A cube has a volume of 125cm (cube)
What is the length of each side of the cube?
Determine the surface area of the cube.
How much paint does Sarah need if 1L covers 30cm(sq)
What are her costs if 1L costs R20
a) 5 x 5 x 5 = 125
The length of each side of the cube is 5cm
b) Surface area of a cube = L x L x 6
= 5 x 5 x 6cm
= 25 x 6cm
= 150cm (sq)
c) 150 / 30
= 5
Sarah needs 5L of paint to cover her cube
d) R20 x 5
= R 100
An L shape measuring:
75cm x 102cm x 32cm x A x B x C
Calculate the area:
A = 51cm B = 43cm C = 51cm
Area = (51cm x 75cm) + (32cm x 51cm)
= 50 x 75 + 75 + 32 x 50 + 32
= 3500 + 250 + 75 + 1500 + 100 + 32
= 3000 + 500 + 200 +50 +70 +5 + 1000 + 500 +100 +30 +2
= 4000 + 1000 + 300 + 100 + 20 + 30 + 7
= 5457cm(sq)
= 54.57m(sq)
Volume of prism 9x9x9cm
Volume = L (cubed)
= 9x9x9cm
= 81cm(sq) x 9
= 810 - 81
= 729cm(cube)
Volume of prism 20m x 3m x 12m
Volume = L x B x H
= 20m x 3m x 12m
= 60m(sq) x 12m
= 600 + 120
= 720m(3)
Volume of a triangular prism
Volume = Area x Height
= (8.5cm x 7cm /2) x 20cm
= (56 + 3.5cm) / 2 x 20cm
=59.5cm / 2 x 20cm
= 595cm (cubed)
= (5600+350) /2 x 200mm
= 5950 / 2 x 200mm
= (2500 + 450 + 25) x 200mm
= 2975 x 200mm
= 595000mm (cubed)
=
