The document discusses the application of similar triangles in various mathematical problems, including finding side lengths in given scenarios. It presents a series of problems involving triangles with known angles and side lengths, as well as real-life applications for measuring heights of objects using proportions. Additionally, it includes questions about identifying similar triangles and calculating corresponding side ratios.

1. SIMILAR
TRIANGLES
APPLICATION

2. Similar Triangles in Math

3. 1. Consider the triangles ABC and PQR. Let BAC ≅ QPR, ABC ≅ PQR, and the
length of each side is as indicated in the figures below. Find the length of QR.
A
B
C
P
Q
R
1
2 1.5
𝑥

4. 2. Consider the triangles ABC and EDC with AB ∥ DE and the length of each side is
as indicated in the figure below. Find the lengths of BC and CE.
A
B
C
D
E
2 cm
1.5 cm
2 cm
4 cm

5. 3. Let AB ∥ DE, AB = 9 cm, BE = 10 cm, EC = 5 cm and DC = 7 cm. Find the length
of AD
A
B C
D
E10 cm 5 cm
9 cm
7 cm

6. 4. Let ABC = BDC, AB = 24 cm, DC = 12 cm, and BC = 16 cm.
Find the length of BD
A
B
CD 12 cm
16 cm
24 cm

7. 5. Let DE ∥ BC. Answer the following questions.
A
B C
D E
F
a. How many triangles are there?
b. Which triangle in the figure is similar to
the triangle ABC? Write down the ratios
of the corresponding sides of those
similar triangles.
c. Which triangle in the figure is similar to
the triangle DEF? Write down the ratios
of the corresponding sides of those
similar triangles.

8. 6. Let ABC = CDE, AB = 13 cm, BC = 25 cm, and CD = 12 cm.
Find the length of DE.
A
B C
D
12 cm
13 cm
E

9. Similar Triangles in Everyday life

10. 1. Supatra is 1.2 meters tall. She is standing 2.5 meters away from an electric
post. Due to the light from the lamp at the top of the electric post, her shadow,
is 1.5 meters long on the ground as shown in the figure below. Find the height
of the electric post.
A
B
D
EC
1.2 m
2.5 m1.5 m

11. 2. Chingchai would like to find the height of a building. He cut a piece of paper
into a right triangle ABC with the legs AC of 30 cm long and BC of 20 cm long.
When he was using this triangle to aim exactly at the top of the building, he
stood 4.5 meters away from the building. See the figure below and find the
height of the building, if the height measured from the ground to the level of
his eyesight is 1.5 meters.
1.5 m
C
B
A
D
E
FG 4.5 m
A
B
C30 cm
20 cm

12. 3. A boy scout lied on the ground holding a cardboard in the shape of right
triangle ABC with the side AB = 1.5 meters and BC = 0.8 meters. He placed the
base of the triangle AB on the ground, which affected AC to be in line with the
top of the flagpole and the top of the building as shown in the figure. Also, the
flagpole is 45 meters away from the building. How much taller is the building
than the flagpole?
A
B
D F
G
E
C
A
B
C
1.5 m
0.8 m
45 m
45 m
H

13. 4. Phasawut would like to find the height of a building. He placed a piece of
mirror in the ground between himself and the building. He can see the top of
the building when the mirror is 4.5 meters away from him and 63 meters away
from the building. The level of Phasawut’s eyes is 1.8 meters high from the
ground. What is the height of the building?
A
B
C
E
D
63 m 4.5 m
1.8 m