Similar Triangles

What does similar mean?

• Similar—the same shapes, but different sizes (may need to be flipped or turned)

4 ft 8ft

4 ft 8ft

12 ft 3ft

6 ft 6 ft

To find the missing side of a triangle:

1) Find corresponding sides of each triangle that you know the measurements for.

2) Find the measurement of the side that corresponds with the missing side.

3) Set up a proportion and solve for the variable.

12 ft 3 ft

16 ft x

A

B C

D

E F

=

=

X=4The missing side measures 4 ft.

Find the missing side s:

• Find the length of side EF:

6.5

• Find the length of the missing side:

• The lengths of each line segment are:• AB = 5• CA= 6• BD= 10• CE= 12• DE= 24

• Find the length of BC

Note: Figures are not drawn to scale.

5 in 3 in

1.8 in x in

Find the missing side:

BD= 8DA= 20AC= xEC= 10EB= 4DE= 6

Word Problems

A tower casts a shadow of 64 feet. A 6-foot tall pole near the tower casts a shadow 8 feet long. How tall is the tower?

A flag pole casts a shadow 3 meters long. A woman near the pole casts a shadow 0.75 meters long. The woman is 1.5 meters tall. How tall is the flag pole?

A magnolia tree measures 25 feet tall. The sun casts a shadow of the tree that measures 42 feet long. A small dogwood tree nearby casts a shadow of 20 feet. What is the height of the dogwood tree?

A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow. How tall is the building? (Round your answer to the nearest tenth.)

Michelle wants to determine the height of a flag pole outside of her school. She places a meter stick next to the flag pole and measures the shadow of the meter stick and flag pole. If the meter stick has a shadow of 140 cm and the flag pole has a shadow of 37.8 meters, how tall is the flag pole?

*Hint: 1 meter=100 cm

Find the missing side:

60.2 x

17.2

7 5

2

• A 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it?

A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow

A 40-foot flagpole casts a 25-foot shadow. Find the shadow cast by a nearby building 200 feet tall.

A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower?

• A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?

x

90 cm 360 cm

160 cm

• The lengths of each line segment are:• AB = 4 in• CA= 6 in• BD= 3 in• CE= 4.5 in• BC= 5 in• Find the length of DE

Note: Figures are not drawn to scale.

BONUS QUESTION!!!

A tree with a height of 4m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 2,000 cm long?

Hint: 1 m = 100 cm