Definition: Similar Triangles
If the measurements of the three angles in two different
triangles are the same, we say the two triangles are similar
triangles.
Rules and Properties: Similar Triangles
If two triangles are similar, their corresponding sides have
the same ratio.
Example 1. Finding the Height of a tree
A man who is 180cm tall casts a shadow that is 60 cm long, how
tall is a tree that casts a shadow that is 9 m long?
Solution:
Note that, because of the sun, the man and his shadow form a
similar triangle to the tree and its shadow. Because of this we can
use the common ratio to find the height of the tree.
180 cm = X
60 cm
9m
1.8 m =
x
0.6 m
9m
X = 1.8 ( 9 ) = 27 m The tree is 27 m tall
0.6X
2. If a man who is 160 cm tall casts a shadow that
is 120 cm long, how tall is a building that casts a
shadow that is 60 m long?
Solution:
160cm = x_
120cm 60m
1.6 m = x_
1.2 m
60 m
X = 1.6(60) = 80 m The building is 80 m tall
1.2
3. Ken is 6 feet tall and his shadow is 10 feet long.The
shadow of the building is 25 feet long. How tall is the
building?
Solution: Using similar triangles to find the height of the building.
Two triangles are similar if all three of its corresponding angles are
congruent.
H =
6 feet
25 feet
10 feet
10h = 25( 6 ) Height of the building = 25( 6 ) = 15 ft.
10
4. A tree casts a shadow 10 feet long. A man 6 ft. tall
was near the tree casts a shadow 4 ft. long.Use
similar triangles to determine the height of the tree?
Solution:
5. A building casts a shadow 50 feet long. A rod 4 feet
tall placed near the building casts a shadow 3 feet
long. Use similar triangle to determine the height of
the building?
Solution:
6.A child 4 feet tall is standing near a street lamp that is 12 feet high.
The light from the lamp casts a shadow of the child. What is the
length of the shadow when the child is 8 feet from the base of the
lamppost?
Solution:
7.A building 50 feet tall casts a shadow 20 feet long. A person 6 feet
tall is walking directly away from the building toward the edge of the
building’s shadow. How far from the building will the person be when
the person’s shadow just begins to emerge from that of the building?
Solution