Similar Triangles

Similar Triangles

Dr. Tom Giles

Similar Triangles

Similar Triangles

Difference in Similar & Congruent

​What does similar mean?

• ​Similar shapes are shapes that each side is scaled up by the same amount (proportional) and all angles are congruent/the same

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​Conditions for similar triangles

• ​AA~

  • ​TWO PAIRS of angles from the triangles are congruent/the same

• ​SAS~

  • ​One angle is congruent to an angle on the other triangle

  • ​The sides on either side of the angle known have same scale factor

• ​SSS~

  • All 3 pairs of sides have same scale factor

Multiple Choice

What is the condition of the similar triangles?

• 3 sides proportional

• ratio of two sides, included $$\angle$$

• A.A.A.

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SSS

• SAS

• Not similar

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• SAS

• AA

• SSS

• not similar

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SSS

• SAS

• no similar

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SAS

• SSS

• not similar

Multiple Choice

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA

• SAS

• SSS

• Not 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 angles 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

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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