Download Similarity-in-Right-Triangles

Geometry
Similarity in Right Triangles—Geometric Mean
Date: __________
Objective: I can find and use relationships in similar right triangles
*Triangle Activity: You will need a ruler and 2 sheets of patty paper.
1) Use one of your patty papers to trace triangle ABC. Label the angles on the patty paper.
2) Use the ruler to draw a line from  B to AC so that the line is perpendicular to AC (this is
called an ___________________.) Label the new point D.
3) What do you notice about the 2 new triangles?
4) Trace triangle ABD and triangle BDC on your second sheet of patty paper. Draw them
separately and label the angles on your patty paper.
5) Use your patty paper to see if any angles of the three triangles are congruent.
6) What can you conclude about the three triangles?
6) Use the diagram below to complete the similarity statement.
RST ~  _______ ~  _______
From the activity, we can conclude that when you draw an altitude in a right triangle, it creates three
similar triangles.
Theorem
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles
that
Proportion for the geometric mean:
The reason all three triangles are similar is by the _______ postulate. The two new triangles have a
____________ angle and at least one angle in common with the original triangle.
In this situation, we have a length that both of the two smaller right triangles share. This length is
called the _________________________. The geometric mean in the diagram above is ______.
For any two positive numbers a and b, the _________________ of a and b is the positive number x
such that:
Most of your answers will not be very nice square roots. We are going to practice simplifying the
square root without decimals (a SLOT from last semester). This is called ____________________
_________________________.
Example 1: Find the geometric mean of 4 and 18.
Ex 2: Find the geometric mean of 15 and 20.
Ex 3: In ABC , AD = 4 and CD = 12. Find BD.
*What does this mean??
Ex 4: To find the height of her school building, Maya held a book near her eye so that the top and
bottom of the building were in line with the edges of the cover. If Maya’s eye level is 5 feet above
the ground and she is standing 10.25 feet from the building, how tall is the building? Round to the
nearest tenth.
Ex 5: Solve for x.
Ex 6: Solve for x.