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

​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

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