Unit 1:Day 6

Day 6: Similar Triangles: Angle to Angle

 

 

This method of determining if shapes are equal is specific to triangles. It's a lot simpler than other shapes; you don't have to make a fraction and cross- multiply. It's simply this: If the triangles' angles are the same, they are similar.

 

In these triangles, even though one is rotated, we know they are similar because they share 2 angles.

This one is more complex because you only have one angle provided. However, it is still easily solvable. Take the 2 side length from each triangle and put them both in a ratio. 21:14 and 15:10 both simplify to the ratio of 3:2, and that along with the shared angle tells us that they're similar.

Just another example.

Quiz Time!

 

1. Are these triangles similar?

 





 

2. What is the angle of C?

 

 

3. What is the length of x? Are the triangles similar?

 

 

 

 

 

 

Key:

 

1. The triangles are similar because the angles all correspond.

 

 

2. Angle C is 70 degrees.

 

 

3. Side x is 24 meters long. We got that because the side 4 was multiplied by 4 to get 16, so the 6 must also be multiplied by 4. The triangles are similar.