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Define the term congruent.
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Define the term congruent.
Two shapes are congruent if they are identical in shape and size.
True or False?
If one shape is an enlargement of the other, then they are congruent.
False.
If one shape is an enlargement of the other, then they are not identical in size and so are not congruent.
True or False?
You need to show that two shapes are facing in the same direction to prove congruence.
False.
If the two shapes are identical in terms of shape and size then it does not matter which direction they are facing in.
What are congruent triangles?
Two triangles are congruent if they are the same size and shape, although they may be reflections, translations, or rotations of each other.
How many corresponding parts in a triangle need to be shown as equal to prove congruence?
Only three of the six corresponding parts (sides or angles) of a triangle need to be shown to be the same to prove congruence.
However, these must be the right three parts.
What does SAS stand for in congruence tests?
SAS stands for Side, Angle, Side.
If two sides and the angle between them can be shown to be the same, then the triangles are congruent.
True or False?
You may need to use facts from topics including parallel lines, symmetry, isosceles triangles, and circle theorems when proving congruence.
True.
You may need to use facts from topics including parallel lines, symmetry, isosceles triangles, and circle theorems when proving congruence.
What does ASA stand for in congruence tests?
ASA stands for Angle, Side, Angle.
If two angles and the side between them can be shown to be the same, then the triangles are congruent.
True or False?
SSA can be used to prove congruence.
False.
SSA can not be used to prove congruence.
Explain the RHS congruence test.
RHS stands for Right angle, Hypotenuse, Side.
Two right-angled triangles can be shown to be congruent if their hypotenuses and one other side can be shown to be the same.
True or false?
SSS can be used to prove congruence.
True.
SSS can be used to prove congruence.
How many standard tests are there to prove congruence?
The five standard tests used to prove congruence are:
SSS (side, side, side)
SAS (side, angle, side)
ASA (angle, side, angle)
AAS (angle, angle, side)
RHS (right-angle, hypotenuse, side)
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