Exploring Similarity in Right Triangles

The video tutorial covers the concept of similarity in right triangles, focusing on how drawing an altitude creates three similar triangles. It explains the angle-angle postulate and demonstrates how to write similarity statements. The tutorial then introduces the geometric mean, explaining its calculation through proportions and solving related problems. The video concludes with examples of finding geometric means and solving proportions in triangles.

What happens when you draw an altitude to the hypotenuse of a right triangle?

• You create two similar triangles.

• You create three similar triangles.

• You create four similar triangles.

• You create no similar triangles.

Which property is used to show that angle A is congruent to itself?

• Symmetric Property

• Transitive Property

• Reflexive Property

• Substitution Property

Why are the small and big triangles similar?

• They have the same hypotenuse.

• They have two congruent angles.

• They have the same area.

• They have the same perimeter.

In the largest triangle, if the hypotenuse is 50, the shorter leg is 22.36, what is the longer leg?

• 50

• 20

• 40

• 44.74

What is the correct similarity statement for the largest triangle?

• Triangle LKM

• Triangle KLM

• Triangle LKJ

• Triangle LMK

What is another name for the arithmetic mean?

• Geometric Mean

• Harmonic Mean

• Average

• Median

How do you find the geometric mean of two numbers?

• Add them together and divide by 2.

• Multiply them together and take the square root.

• Subtract the smaller from the larger.

• Divide the larger by the smaller.

What is the geometric mean of 2 and 18?

• 4

• 8

• 6

• 10

In the proportion 2/x = x/18, what is the value of x?

• 3

• 6

• 4

• 5

What is the geometric mean of 4 and 12?

• 7.5

• 6.93

• 8.5

• 5.5