Congruent and Similar Figures

Two figures are congruent if a series of transformations can be used to map one figure onto the other

These two triangles are congruent because a translation can map the blue triangle (ABC) to the red triangle (A'B'C')

These two triangles are similar because DEF can be mapped to ABC through a dilation, rotation, and translation

Note the symbol to indicate two figures are similar

Congruence and similarity can be used to find missing measures in figures.

Because we are told the figures are congruent, we can find the missing angle by looking at the corresponding part. 

<N corresponds to <S (by rotating the figure) so <N=136

To find missing sides using similarity, you must first find the scale factor or common ratio between the corresponding sides

As you see in the example, all of the sides have a ratio of 1/2 comparing the small triangle to the large triangle

All of the angle are the same as is true in all similar figures.

To find the value for x, the ratio must be the same as the other sides shown.

The scale factor is 2 so 2x8=16. 16 would be the value for x.

You try to find the value for y and enter it on the next slide