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Geometry: Unit 6
Notes: Similarity in Right Triangles
Name:
An ALTITUDE is a segment drawn from a vertex to the opposite side. It intersects the opposite side at a right
angle.
The altitude of ∆𝐴𝐶𝐵is _____________.
Investigation
The altitude to the hypotenuse has been constructed in each right triangle below. Find the measures of the missing
angles.
Discuss the following questions with your group:
1. How do the smaller right triangles compare in each diagram?
2. How do they compare to the original right triangle?
Conjecture:
The altitude to the hypotenuse of a right triangle divides the triangle into two smaller right triangles that are
_____________________ to each other and to the original ________________________.
Example #1
a. In the diagram, outline each of the three triangles in a different color. Then name these three triangles
appropriately in a similarity statement.
b. Find the value of x.
Example #2
a. In the diagram, outline each of the three triangles in a different color. Then draw the three triangles.
b. Find the value of the variables.
Practice!!!
1.
2.
y
3.
4.
m