Åk 6–9
 
English/عربي
2.1 Congruent and Similarity

Congruent
Figures which have the same form and are exactly the same size are called congruent. You could even say that they are copies of each other.



Rectangle A is congruent to rectangle B.
There measurements are identical: 5 cm x 3 cm.




Similarity

Figures which have the same form but that don’t have the same size are called similar. You can say that they have the same form and the same proportions.



In every rectangle, the length is twice as long as the width.  The relationship between length and width in the rectangles is the same.

2
=
4
=
6
 
1
2
3

The rectangles A, B and C are similar.






“Top Triangle” Theorem

In the triangle ABC, the length DE is parallel to the side BC.
DE is called for a parallel transversal because it intersects two sides of the triangle ABC and is parallel to the line BC.

The parallel transversals creates a “top triangle” ADE, which is similar to the large triangle ABC.
Similarity gives:

AD relates to AB, as
AE relates to AC, as
DE relates to BC.