What is a bearing?
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What is a bearing?
A bearing is a way of describing and using a direction as an angle.
From which compass direction should a bearing always be measured?
A bearing should always be measured from North.
True or False?
Bearings are measured in an anti-clockwise direction.
False.
Bearings are measured in a clockwise direction.
How many figures must a bearing be written with?
A bearing must be written with 3 figures.
For angles under 100°, zero(es) should be used to fill in the missing figures, e.g. 059º, 008º.
Which two triangle methods are frequently used in bearings questions?
Pythagoras' theorem and SOHCAHTOA are frequently used in bearings questions. This is because situations often include right-angled triangles.
True or False?
You should always draw a diagram when answering questions involving bearings.
True.
You should always draw a diagram when answering questions involving bearings.
True or False?
You will always need a protractor for bearings questions.
False.
A protractor is an essential piece of equipment for measuring bearings to scale, but they are not always required in every bearings question.
For example, a diagram may give you a bearing then ask you to find another angle, which you could find using angle properties instead of a protractor.
Which compass direction is indicated by a bearing of 090°?
When a bearing is 090°, it means due east.
True or False?
North should always be indicated on a diagram.
True.
North should always be indicated on a diagram as a point of reference.
What is the definition of scale in geometry?
The scale is the ratio used to convert real-life objects into accurate drawings.
True or False?
Maps and technical drawings are usually drawn to a scale.
True.
Maps and technical drawings are usually drawn to a scale.
What does it mean when a scale is given as a ratio, e.g. a scale of 1:10,000?
When the scale is given as a ratio (e.g., 1:10,000), it means that 1 unit on the diagram represents 10,000 of the same type of units in real life.
How is a scale length on a map converted to a real-life length?
To convert from a scale length to a real length, multiply by the scale factor.
What is the definition of a scale drawing?
A scale drawing is a representation of an object or area that is drawn to a specific scale or ratio.
How is a real-life length converted to a scale length on a map?
To convert from a real length to a scale length, divide by the scale factor.
True or False?
It may be helpful to convert the scale to more suitable units when dealing with very small or large scales.
True.
It may be helpful to convert the scale to more suitable units when dealing with very small or large scales.
For example, if 1 cm on a map represents 25,000 cm in real-life, it may be easier to convert the units to 250 m or 0.25 km.
True or False?
Map scales are always given with units.
False.
Map scales are usually given in the form 1:n with no reference to units.
True or False?
Bearings are often used on maps.
True.
Bearings are often used on maps in order to indicate direction.
What is the definition of a construction?
A construction is an accurate drawing that normally uses equipment such as a sharp pencil, a ruler, a protractor, and/or a pair of compasses.
What is an SSS triangle?
An SSS triangle is a triangle where you are given the lengths of all three sides.
What equipment do you need to accurately construct an SSS triangle?
Drawing an accurate SSS triangle requires the following equipment: a sharp pencil, a ruler and a pair of compasses.
True or False?
Once you have constructed a given triangle you must erase the construction lines.
False.
To get full marks, you must leave your construction lines on your drawing as evidence of your working.
What is an SAS triangle?
An SAS triangle is a triangle where you are given the length of two sides and the size of the angle in between them (the included angle).
True or False?
You need a sharp pencil, a ruler and a pair of compasses to accurately construct an SAS triangle?
False.
You do need a sharp pencil and a ruler, but you need a protractor rather than a pair of compasses in order to measure the angle.
What is an ASA triangle?
An ASA triangle is a triangle where you are given the size of two angles and the length of the side in between them (the included side).
Define the term equidistant.
Equidistant means at an equal distance.
For example, all the points on the circumference of a circle are equidistant from the centre of the circle.
True or False?
You can construct a unique triangle given the size of all three angles.
False.
You cannot construct a unique triangle given the size of all three angles.
Using this information you could draw an infinite number of different triangles that are all enlargements of one another.
True or False?
A unique triangle cannot be constructed given the length of two sides and an angle that is not the included angle.
True.
A unique triangle cannot be constructed given the length of two sides and an angle that is not the included angle.
This information is ambiguous as two distinct triangles could be constructed from it.
What does it mean to bisect a line segment?
To bisect a line segment means to divide it into two equal parts.
Define the term perpendicular bisector.
A perpendicular bisector is a line that cuts another line exactly in half (bisect) and crosses it at a right angle (perpendicular).
What are the steps for constructing a perpendicular bisector?
To construct a perpendicular bisector, you should do the following:
Set the distance between the point of the compasses and the pencil to be more than half the length of the line
Place the point of the compasses on one end of the line and sketch an arc above and below the line
Keeping your compasses set to the same distance, move the point of the compasses to the other end of the line and sketch an arc above and below it again, the arcs should intersect each other both above and below the line
Connect the points where the arcs intersect with a straight line
What is the definition of an angle bisector?
An angle bisector is a line that cuts an angle exactly in half (bisects the angle).
What are the steps for constructing an angle bisector?
To construct an angle bisector you should do the following:
Set the distance between the point of the compasses and the pencil to be about half the distance of the lines forming the angle
Place the point of the compasses at the point of the angle and sketch an arc that intersects both of the lines that form the angle
Place the point of the compasses on one of the points of intersection and sketch an arc
Keeping the distance between the point of the compasses and the pencil the same, sketch an arc with the point of the compasses on the other point of intersection, the arcs should intersect
Join the point of the angle to the point of intersection of the arcs with a straight line
True or False?
The process for constructing an angle bisector is a variation on the process for constructing a perpendicular bisector.
True.
The process for constructing an angle bisector is a variation on the process for constructing a perpendicular bisector.
The first step of constructing an angle bisector is to sketch arcs on the lines that form the angle. To bisect the angle, you then effectively construct a perpendicular bisector of the straight line formed between these two arcs.
What equipment do you need to construct a perpendicular bisector or an angle bisector?
To construct a perpendicular bisector or an angle bisector, you need a sharp pencil, a ruler, and a pair of compasses.
True or False?
A protractor is required to construct a perpendicular bisector or an angle bisector.
False.
You should not use a protractor to measure any angles whilst constructing a perpendicular bisector or an angle bisector.