If one or more of these 4 conditions hold then the two triangles are congruent:
1. SSS - three sides are the same
2. AAS - two angles and a side match up
3. SAS - two sides and an angle match up
4. RHS - a right angle, the hypotenuse and one other side match up
For scale factor 'n' :
The sides are n times bigger
The areas are n squared times bigger
The volumes are n cubed times bigger
2 spheres have surface areas of 16m squared and 25m squared. Find the ratio of their volumes.
Area = a squared : b squared = 16 : 25
Therefore... a : b = 4 : 5
Therefore... a cubed : b cubed = 64 :125
Volume of the spheres = 64m cubed and 125m cubed
How to remember the 4 transformations
T = Translation
E = Enlargement
R = Rotation
R = Reflection
When an object is translated all that changes is the position of the object.
You must specify the vector of the translation.
When an object is enlarged all that changes is the size (unless it is a negative scale factor because then the orientation changes also)
You must specify the scale factor and the centre of enlargement.
When an object is rotated all that changes is the position and orientation.
You must specify the angle turned, the direction turned and the centre of rotation.
When an object is reflected all that changes is the position and orientation.
You must specify the mirror line.