Congruent and Similar Figures

Congruent and Similar Shapes

Congruence

Figures are congruent if all corresponding parts are congruent or equal.

Transformations that maintain congruence (do not change size of the figure):

- translations

- rotations

- reflections

Corresponding parts of congruent shapes are congruent.

Using Transformations to prove congruence

• 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')

Multiple Select

Which transformations maintain congruence?

• Dilations

• Translations

• Rotations

• Reflections

Similar Figures

Figures are similar if the corresponding parts are proportional. In other words, there is a common ratio between the corresponding parts of the figures (scale factor of the dilation)

Similar figures are the same shape but different sizes. Dilations can be used to map one similar figure onto another

Similar Figures

• 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

Multiple Choice

Similar shapes have the same side and angle measures.

• True

• False

Multiple Choice

Similar shapes have a common ratio or scale factor between their corresponding components

• True

• False

Multiple Select

Which transformation(s) create two similar figures.

• dilation

• translation

• rotation

• reflection

Using Congruence and Similarity to solve problems

• 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

Multiple Choice

What is the measure of CD?

• 81

• 50

• 96

Using Similarity to solve problems

• 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.

Using Similarity to solve problems

• 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

Fill in the Blank

What is the value for y?

Multiple Select

What is true about congruent figures

• one figure can be mapped to the other through a series of transformations

• there is a common ratio between corresponding parts

• all angles are the same

• all sides are the same

• a dilation can be used to map one figure to the other

Multiple Select

What is true about similar figures

• one figure can be mapped to the other through a series of transformations

• there is a common ratio between corresponding parts

• all angles are the same

• all sides are the same

• a dilation can be used to map one figure to the other