Proportionality and Similar Shapes

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

Fill in the Blank

$\Delta$ ABC ~ $\Delta$ _ _ _

Fill in the Blank

$$\Delta$$  ABC ~  $$\Delta$$  _ _ _

​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