Similar Figures (Online Tutorial #21)

Similar Figures and their Proportionality

Multiple Choice

This symbol stands for ...

• is corresponding to
• is proportional to
• is congruent to
• is similar to

Multiple Choice

This symbol stands for ...

• similar
• congruent
• proportional
• corresponding

• During translations, reflections, and rotations, the pre image and image are congruent

• During a dilation, the pre image and image are similar. Let's talk about the difference...

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Congruent vs Similar

Congruent figures are both the same size and the same shape. Therefore all the side lenghts of the image are the same as the pre image.

​​Congruent

​SImilar figures are the same shape but different sizes. What's special about them is their proportionality.

​​Similar

We can set up proportions of corresponding sides of similar figures to solve for a missing side length.

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Similar Figures

• same shape, different size

• think blowing up or shrinking an image on a copier

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.

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

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

Visual:

Subject | Subject

Some text here about the topic of discussion

Similar Shapes

Have equal angles and proportional sides

Equal Angles

Triangles have interior angles that add up to 180 degress

​Remember

All the sides use the same rule

​Similar if...

Similarity

Multiply or divide by the scale factor to find the missing length

​Find the missing side

Divide the known corresponding lengths to find the scale factor
Tips: make sure you are comparing matching sides
Double check if you should be multiplying or dividing

​First, identify the rule

Finding Missing Side Lengths