Right Triangle Similarity and Geometric Mean Lesson

Similarity in Right Triangles

Lets work this one together

Lets work this one together

Multiple Choice

Find x

• 15

• 12

• 9.9

• 6

Multiple Choice

Find x

• 6.72

• 5

• 15

• 8.12

Multiple Choice

Which one is the definition for geometric mean?

• two positive numbers, a and b such that $$\frac{a}{b}=\frac{x}{x}$$

• two positive numbers, a and b such that $$\frac{a}{x}=\frac{x}{b}$$

Let's do one together

6 and 30

Multiple Choice

16 and 28

• $$\sqrt{447}=8\sqrt{7}$$

• $$\sqrt{180}=6\sqrt{5}$$

• .57

• $$\sqrt{.57}$$

Multiple Choice

Insert one geometric mean between 4 and 100.

• 15

• -25

• 20

• -20

Multiple Choice

Find the geometric mean for 2 and 25.

• 5
• 2√5
• 2
• 5√2

Multiple Choice

Find the geometric mean for 4 and 9.

• 6
• 2√3
• 3√2
• 8

Multiple Choice

12 and 50

• 25

• $$\sqrt{1050}=32.40$$

• $$\sqrt{600}=10\sqrt{6}$$

• 5

Multiple Choice

Which is the geometric mean for this triangle?

• $$AD=BD*DC$$

• $$BD^2=AD\cdot DC$$

• $$BD=AD\cdot DC$$

• $$BC=AD*BD$$

Let's do this one together!

Let's do this one together!

Multiple Choice

Find X.

• 1.2

• 270

• 21.6

• 3

Multiple Choice

Find X.

• 30+14.7=44.7

• 51

• 14.7

• 30-21=9

Multiple Select

What is the geometric mean of this triangle using the Leg Theorem?

SELECT ALL THAT APPLY

• $$AB^2=AD\cdot AC$$  

• $$AB\cdot AC=DC$$  

• $$DC^2=AB\cdot AC$$  

• $$BC^2=DC\cdot AC$$  

Let's do this one together

Let's do this one together!

Multiple Choice

Find X.

• $$\sqrt{10}$$

• $$\sqrt{56}=2\sqrt{15}$$

• $$56$$

• $$\sqrt{\frac{7}{2}}$$

Multiple Choice

Find X.

• 56

• $$\sqrt{56}$$

• $$\sqrt{252}=6\sqrt{7}$$

• $$\sqrt{10}$$

Multiple Select

What is a possible equation for solving for y?

more than one correct answer

• $$\frac{12}{y\ }=\frac{y}{4}$$

• $$\frac{12}{4}=\frac{y}{x}$$

• $$\frac{4}{y\ }=\frac{y}{12}$$

• $$\frac{x}{4\ }=\frac{12}{x}$$

• y = 48

Multiple Select

What is a possible equation for solving for x?

more than one correct answer

• $$\frac{4}{x\ }=\frac{x}{16}$$

• $$\frac{4}{x\ }=\frac{x}{12}$$

• $$\frac{16}{x\ }=\frac{x}{4}$$

• $$\frac{x}{4}=\frac{4}{y}$$

Multiple Choice

Which triangle is similar to $$\Delta ABC$$  ?

• $$\Delta CBA$$  

• $$\Delta DAC$$  

• $$\Delta DCA$$  

• $$\Delta CBA$$  

Multiple Choice

• A
• B
• C
• D

Multiple Choice

How far is it across the lake?

• 4

• 6

• 9

• 12

Multiple Choice

In the accompanying diagram of right triangle ABC, CD is drawn perpendicular to hypotenuse AB. If AB=16 and DB=4 find the length of BC.

• 0

• 8

• 32

• 64

Multiple Choice

Solve for x.

Leave in simplest radical form

• 8

• 10

• 64

• $$4\sqrt[]{3}$$  

Multiple Choice

• A
• B
• C
• D