Similarity and Indirect Measurement

Similarity and Indirect Measurement

Corresponding sides make a fraction. Two fractions set equal make a proportion.

4 correct proportions

Use the Similarity Statement to write a proportion. Corresponding letters will be corresponding sides.

Multiple Select

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. Which statements are correct?

• CE is porportional to EA

• $$\frac{4}{8}=\frac{5}{x}$$  
  

• $$\frac{4}{12}=\frac{5}{x}$$  

• CE is Proportional to CA

Multiple Choice

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter?

• 10

• 12

• 15

• 18

Right triangles are used to represent height and shadows. What is the height of the larger triangle?

Multiple Select

At the same time a 6 foot person casts a 2 foot shadow, a nearby tree casts a ten foot shadow. How tall is the tree? Which statements are correct?

• The situation can be represented by 2 similar right triangles.

• The large triangle will be formed by the tree and its shadow.

• The smaller triangle will be formed by the person and their shadow.

• Shadows lie on the ground & are drawn as the base of the triangle.

Multiple Select

At the same time a 6 foot person casts a 2 foot shadow, a nearby tree casts a ten foot shadow. How tall is the tree? Which statements are correct?

• $$\frac{\left(t\right)\ height}{\left(\ t\right)\ shadow}=\frac{\left(p\right)\ height}{\left(p\right)\ shadow}$$

• $$\frac{\left(t\right)height}{\left(p\right)height}=\frac{\left(t\right)shadow}{\left(p\right)shadow}$$
  

• $$\frac{\left(t\right)height}{\left(t\right)shadow}=\frac{\left(p\right)shadow}{\left(p\right)height}$$

Multiple Select

At the same time a 6 foot person casts a 2 foot shadow, a nearby tree casts a ten foot shadow. How tall is the tree? Which statements are correct?

• $$\frac{\left(t\right)\ height\ x}{\left(\ t\right)\ shadow\ 10}=\frac{\left(p\right)\ height\ 6}{\left(p\right)\ shadow\ 2}$$

• $$\frac{\left(t\right)height\ x}{\left(p\right)height\ 6}=\frac{\left(t\right)shadow\ 10}{\left(p\right)shadow\ 2}$$
  

• $$\frac{\left(t\right)height\ x}{\left(t\right)shadow\ 10}=\frac{\left(p\right)shadow\ 2}{\left(p\right)height\ 6}$$

Multiple Choice

At the same time a 6 foot person casts a 2 foot shadow, a nearby tree casts a ten foot shadow. How tall is the tree? Which statements are correct?

• 3 feet

• 10 feet

• 16 feet

• 30 feet

Multiple Choice

If you are using indirect measurement, what is true?

• You must convert dimensions to the same unit of measurement.

• You do not have to convert dimensions to the same unit of measurement.

Multiple Select

A tree outside Ellie's building cast a 125 foot shadow. At the same time of the day, Ellie cast a 5.5 foot shadow. If Ellie is 4ft 10 in tall, how tall is the tree? Which statements are correct?

• 4 ft 10 in = 4.10 in

• 4 ft 10 in = 4.8333 in

• divide 10 inches by 12 to convert to feet

• divide 4 ft by 12 to convert to inches

Multiple Select

A tree outside Ellie's building cast a 125 foot shadow. At the same time of the day, Ellie cast a 5.5 foot shadow. If Ellie is 4ft 10 in tall, how tall is the tree? Which statements are correct?

• $$\frac{height\left(sm\right)}{height\left(\lg\right)}=\frac{shadow\left(sm\right)}{shadow\ \left(\lg\right)}$$
  

• The large triangle is formed by the height and shadow of the tree.

• The small triangle is formed by Ellie's height and her shadow.

• $$\frac{height\left(\lg\right)}{shadow\left(\lg\right)}=\frac{height\left(sm\right)}{shadow\ \left(sm\right)}$$

Multiple Select

A tree outside Ellie's building cast a 125 foot shadow. At the same time of the day, Ellie cast a 5.5 foot shadow. If Ellie is 4ft 10 in tall, how tall is the tree? Which statements are correct?

• $$\frac{height\left(sm\right)}{height\left(\lg\right)}=\frac{shadow\left(\lg\right)}{shadow\ \left(sm\right)}$$
  

• $$\frac{x}{4.83}=\frac{125}{5.5}$$  
  

• $$\frac{x}{125}=\frac{4.83}{5.5}$$  
  

• $$\frac{height\left(\lg\right)}{shadow\left(\lg\right)}=\frac{height\left(sm\right)}{shadow\ \left(sm\right)}$$

Multiple Choice

A tree outside Ellie's building cast a 125 foot shadow. At the same time of the day, Ellie cast a 5.5 foot shadow. If Ellie is 4ft 10 in tall, about how tall is the tree? 

• $$\frac{height\left(sm\right)}{height\left(\lg\right)}=\frac{shadow\left(\lg\right)}{shadow\ \left(sm\right)}$$  

• $$\frac{x}{4.83}=\frac{125}{5.5}$$  
  

• $$\frac{x}{125}=\frac{4.83}{5.5}$$  
  

• $$\frac{height\left(\lg\right)}{shadow\left(\lg\right)}=\frac{height\left(sm\right)}{shadow\ \left(sm\right)}$$  
  

Multiple Choice

A man is 6 feet tall and his shadow is 2 feet long.

How long is the shadow of a 5 feet tall woman?

(Hint: make a picture of two right triangles)

• 15 feet

• 2.4 feet

• 1.6 feet

• 1 foot

Multiple Choice

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet
• 72 feet
• 36 feet

Multiple Select

DE ll BC. Parallel lines separate the sides proportionally. The following statements are true. Select all

• AE is proportional to EC

• $$\frac{AE}{EC}=\frac{AD}{DB}$$

• AD is proportional to DB

• $$\frac{X}{15}=\frac{10}{12}$$

Multiple Choice

Find AE

• 12.5

• 18

• 11.75

• 13