Geometric Mean of Right Triangles

​Similar Triangles, Geo Mean & Pythagorean Theorem

Multiple Choice

$$\Delta ABC\ \sim\ \Delta MTS$$

Complete the statement: $$\angle A\ \cong\ \angle\$$ ____

• B

• M

• T

• S

Multiple Choice

$$\Delta ABC\ \sim\ \Delta MTS$$

Complete the statement: $$\angle T\ \cong\ \angle\$$ ____

• A

• B

• C

• M

Multiple Choice

$$\Delta ABC\ \sim\ \Delta MTS$$

Complete the statement: $$\frac{AB}{?}=\ \frac{?}{MS}$$ ____

• $$\frac{AB}{MT}=\ \frac{AC}{MS}$$

• $$\frac{AB}{MT}=\ \frac{BC}{MS}$$

• $$\frac{AB}{AC}=\ \frac{BC}{MS}$$

• $$\frac{AB}{BC}=\ \frac{MT}{MS}$$

Fill in the Blank

Find the geometric mean of 8 and 32,

Multiple Choice

What is geometric mean of 4 and 9?

• 5

• 6

• 7

• 8

Multiple Choice

Find the geometric mean for 2 and 25.

• 5

• 2√5

• 2

• 5√2

Multiple Choice

What is the formula used to solve for the hypotenuse?

• a²⁺b²=c²

• a+b=c

• a-b=c

• c-a=c

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse

• scalene

• isosceles

• right

Multiple Choice

What is the opposite of squaring a number?

• divide

• multiply 

• fractions

• square root

Multiple Choice

solve for the value of y

• 13

• 5

• 23

• 10

Multiple Choice

solve for x

• 5552363959656.

• 10

• 100

• 89

Multiple Choice

Identify the correct similar triangles

• $$\Delta GEF\sim\Delta HGF\sim\Delta HEG$$

• $$\Delta FGE\sim\Delta FGH\sim\Delta GHE$$

• $$\Delta GEF\sim\Delta HFG\sim\Delta HEG$$

• $$\Delta FGE\sim\Delta FHG\sim\Delta GEH$$

Multiple Choice

Identify the correct similar triangles

• $$\Delta QSR\ \sim\Delta STQ\sim\Delta TRS$$

• $$\Delta QSR\sim\Delta TSQ\sim\Delta STR$$

• $$\Delta QSR\sim\Delta QTS\sim\Delta STR$$

• $$\Delta RSQ\sim\Delta TSQ\sim\Delta TSR$$

​ (part of hypotenuse)

Multiple Choice

To solve for x, do you use:

Altitude Rule or Leg Rule?

• Altitude Rule

• Leg Rule

Multiple Choice

To solve for x, do you use:

Altitude Rule or Leg Rule?

• Altitude Rule

• Leg Rule

Multiple Choice

To solve for x, do you use:

Altitude Rule or Leg Rule?

• Altitude Rule

• Leg Rule

Multiple Choice

To solve for x, do you use:

Altitude Rule or Leg Rule?

• Altitude Rule

• Leg Rule

Multiple Select

What is a possible equation for solving for y?

• $$\frac{12}{y\ }=\frac{y}{4}$$

• $$\frac{12}{4}=\frac{y}{x}$$

• $$\frac{4}{y\ }=\frac{y}{12}$$

• $$\frac{x}{4\ }=\frac{12}{x}$$

• y = 48

Multiple Select

Choose answer choices for x and y. Round to the nearest tenth if necessary.

Take. your. time.

• y = 4.5

• y = 10

• x = 6

• x = 6.5

• y = 3.3

Multiple Choice

Find the value of w and x.

• w = 16, y = 2

• w = 2, y = 17

• w = 3, y = 15

• w = 2, y = 18

• w = 2, y = 16

Multiple Choice

Find the value of x.

• 21

• 3

• 81

• 9

• 18

Multiple Choice

Find the value of y.

• 6

• 108

• $$6\sqrt{6}$$

• $$3\sqrt{6}$$

• 3

Multiple Choice

$$\overline{BD}$$  is the altitude of  $$\Delta ABC$$  . If AD=25, BD=10, then what is AC?

• 5

• 4

• $$5\sqrt{10}$$  

• 29

• $$10\sqrt{5}$$  

Multiple Choice

A cross section of a group of seats at a stadium shows a drainage pipe  $$\overline{BD}$$  that leads from the seats to the inside of the stadium.  What is the approximate length of the pipe?

• 60 feet

• 16.6 feet

• 3.6 feet

• 15.6 feet

• 10.3 feet

Multiple Choice

Which statement is NOT true?

• $$\Delta KLM\sim\Delta JLK$$

• $$\Delta JLK\sim\Delta JKM$$

• $$\Delta JKM\sim\Delta KLM$$

• $$\Delta MLK\sim\Delta MJK$$

Multiple Choice

Which statement is NOT true?

• $$\Delta XUY\sim\Delta ZUY$$

• $$\Delta YXU\sim\Delta ZXY$$

• $$\Delta ZXY\sim\Delta ZYU$$

• $$\Delta ZYU\sim\Delta YXU$$

Multiple Choice

Find the missing length indicated. Leave your answer in simplest radical form.

• 60

• 100

• 80

• 20

Multiple Choice

Find the missing length indicated. Leave your answer in simplest radical form.

• 64

• 12

• 9

• 100

Multiple Choice

Find the missing length indicated. Leave your answer in simplest radical form.

• 48

• 16

• 80

• 36

Multiple Choice

Complete and solve the proportion

• ? = 5 and x=5√3

• ? = 20 and x=10√3

• ? = 35 and x=5√21

• ? = 15 and x = 5

• Not enough information given

Multiple Choice

Complete and solve the proportion

• ? = 20 and x=30

• ? = 18 and x=27

• ? = 12 and x=18

• ? = 8 and x=12

• Not enough information given

Multiple Choice

Complete and solve the proportion

• ? = 2 and x=3√2

• ? = 9 and x=11

• ? = 11 and x=3√11

• ? = 20 and x= 6√5

• Not enough information given

Multiple Choice

Complete and solve the proportion

• ? = 20 and x=30

• ? = 18 and x=27

• ? = 12 and x=18

• ? = 8 and x=12

• Not enough information given

Multiple Choice

Find the value of the variable. Round to the nearest hundredth.

• 2

• 2.5

• 3

• 3.5

• 4

Multiple Choice

Find the value of the variable. Round to the nearest hundredth.

• 6

• 6.93

• 7

• 7.20

• 7.32

Multiple Choice

Find the value of the variable. Round to the nearest hundredth.

• 2

• 3

• 3.5

• 3.81

• 4.17

Multiple Choice

Find the length of AC

• 18

• 24

• 32

• 48

• 50