Congruence, Similarity & Geometrical Proof (Edexcel IGCSE Maths B): Flashcards
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Define the term similar shapes.
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Define the term similar shapes.
Two shapes are similar if they have the same shape and their corresponding sides are in proportion.
One shape is an enlargement of the other.
True or False?
If two triangles of different sizes have the same angles they are not similar.
False.
If two triangles of different sizes have the same angles they are similar.
One is an enlargement of the other.
True or False?
Shapes that are not triangles can have the same angles and not be similar.
True.
Some shapes that are not triangles can have the same angles and not be similar.
E.g. two rectangles of different sizes will have the same angles but their corresponding sides could have different scale factors.
True or False?
To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.
True.
To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.
What is a scale factor, in the context of similarity?
A scale factor is the ratio of corresponding lengths in similar shapes.
True or False?
In the context of similarity, a scale factor cannot be negative.
True.
Although you can have a negative scale factor in general enlargement, in the context of similarity, a scale factor cannot be negative.
What does a scale factor that is greater than 0 but less than 1 imply?
A scale factor that is greater than 0 but less than 1 implies that the similar shape is smaller than the original shape.
How can you find a length scale factor?
A length scale factor can be found by dividing the length of a side on one shape by the length of a corresponding side on the similar shape.
What is a geometrical proof?
A geometrical proof involves using known rules about geometry to prove a new statement about geometry.
How should each step in a geometrical proof be written?
Each step should be written in the form "[fact], [mathematical reason]".
It is really important to give a reason for each fact that you state.
E.g. Angle ABE = Angle CDE = 60º, vertically opposite angles.
There are a number of different rules or facts that you can use in geometrical proof.
Name three types of rules.
Any of the following types of rules may be used in geometrical proof:
Properties of 2D shapes (especially isosceles triangles and quadrilaterals)
Basic angle properties
Angles in polygons
Angles in parallel lines
Congruence and similarity
Circle theorems
Pythagoras' theorem
What does it mean when a scale for a diagram 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.
E.g. 1 cm on map = 10, 000 cm (or 100 m) in real life
How is a scale length on a map converted to a real-life length?
E.g. a length of 3 cm on a map with scale 1 : 20, 000.
To convert from a scale length to a real length, multiply by the scale factor.
E.g. 3 × 20 000 = 60 000 cm (600 m).
How is a real-life length converted to a scale length on a map?
E.g. a real-length of 15 km using a map with scale 1 : 50, 000.
To convert from a real length to a scale length, divide by the scale factor.
E.g. 15 ÷ 50, 000 = 0.000 3 km (30 cm).
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 and use 1 cm represents 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.
What is meant by a "scale drawing"?
A scale drawing uses a given scale (e.g. 1 : 300) to produce an accurate drawing of a real life object.
They are used when designing a vehicle or a building.
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