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Similar Triangles
Slide 1
Points to remember:
• The sum of the angles of a triangle is 180
• If two corresponding angles in two triangles are equal, the third angle will
also be equal.
• Two triangles are similar if
o any two of the three corresponding angles are congruent
o or one pair of corresponding angles is congruent and the
corresponding sides adjacent to the angles are proportional.
• Two right triangles are similar if one pair of corresponding angles is
congruent.
Slide 2
Example 1:
If DCE ~ VUW, find the measure of .CD
Slide 3
Example 1:
If DCE ~ VUW, find the measure of .CD
List the corresponding sides:
and
and
and
DC VU
DE VW
CE UW
Slide 4
Example 1:
If DCE ~ VUW, find the measure of .CD
List the corresponding sides:
and
and
and
DC VU
DE VW
CE UW
Set up the proportion and solve…
12 9
36 x

12 324x 
1
12 12
2 324x

27x 
OR
36
12 9
x

324 12x
3
12 12
24 12x

27x 
Slide 5
Example 2:
The triangles are similar. Calculate the missing side.
If 42 and 30, then 12FH RH FR  
12
Let x = length of 𝐹𝑆
12
84 42
x

42 1008x 
42 10
42 42
08x

24x 
Slide 6
Example 2:
The triangles are similar. Calculate the missing side.
If 42 and 30, then 12FH RH FR  
12
Let x = length of 𝐹𝑆
12
84 42
x

42 1008x 
42 10
42 42
08x

24x 
24
FS SG FG 
24 84SG 
60SG 
Answer:
The missing side has a measure of 60.
Slide 7
10.5
Example 3:
ABC ~ DEF. Find the missing sides and missing angles.
Slide 8
10.5
Example 3:
ABC ~ DEF. Find the missing sides and missing angles.
Since the triangles are similar, the
corresponding angles are congruent.
82
A D
A
  
   34
C F
F
  
  
Angles in a triangle add up to 180
180
82 34 180
64
A B C
B
B
      
    
  
Slide 9
10.5
Example 3:
ABC ~ DEF. Find the missing sides and missing angles.
Since the triangles are similar, the
corresponding angles are congruent.
82
A D
A
  
   34
C F
F
  
  
Angles in a triangle add up to 180
180
82 34 180
64
A B C
B
B
      
    
  
Corresponding sides
are proportional.
Set up the proportion…
10.5
7 12
y

7 126y 
18y 
10.5
7 14
z

7 147z 
21z 
Slide 10
Example 4:
Tom wants to find the height of a tall evergreen tree. He places a
mirror on the ground and positions himself so that he can see the
reflection of the top of the tree in the mirror. The mirror is 0.7 m
away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall
is the tree? Note: the triangles are similar.
Set up the proportion and solve…
Slide 11
Example 4:
Tom wants to find the height of a tall evergreen tree. He places a
mirror on the ground and positions himself so that he can see the
reflection of the top of the tree in the mirror. The mirror is 0.7 m
away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall
is the tree? Note: the triangles are similar.
Answer:
The tree would be 14.14 m tall.
1.8 0.7
5.5h

0.7 9.9h 
0.7
0.7 9
.7
.9
0
h

14.14h 

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MWA 10 6.4 Similar Triangles

  • 1. Similar Triangles Slide 1 Points to remember: • The sum of the angles of a triangle is 180 • If two corresponding angles in two triangles are equal, the third angle will also be equal. • Two triangles are similar if o any two of the three corresponding angles are congruent o or one pair of corresponding angles is congruent and the corresponding sides adjacent to the angles are proportional. • Two right triangles are similar if one pair of corresponding angles is congruent.
  • 2. Slide 2 Example 1: If DCE ~ VUW, find the measure of .CD
  • 3. Slide 3 Example 1: If DCE ~ VUW, find the measure of .CD List the corresponding sides: and and and DC VU DE VW CE UW
  • 4. Slide 4 Example 1: If DCE ~ VUW, find the measure of .CD List the corresponding sides: and and and DC VU DE VW CE UW Set up the proportion and solve… 12 9 36 x  12 324x  1 12 12 2 324x  27x  OR 36 12 9 x  324 12x 3 12 12 24 12x  27x 
  • 5. Slide 5 Example 2: The triangles are similar. Calculate the missing side. If 42 and 30, then 12FH RH FR   12 Let x = length of 𝐹𝑆 12 84 42 x  42 1008x  42 10 42 42 08x  24x 
  • 6. Slide 6 Example 2: The triangles are similar. Calculate the missing side. If 42 and 30, then 12FH RH FR   12 Let x = length of 𝐹𝑆 12 84 42 x  42 1008x  42 10 42 42 08x  24x  24 FS SG FG  24 84SG  60SG  Answer: The missing side has a measure of 60.
  • 7. Slide 7 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles.
  • 8. Slide 8 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles. Since the triangles are similar, the corresponding angles are congruent. 82 A D A       34 C F F       Angles in a triangle add up to 180 180 82 34 180 64 A B C B B               
  • 9. Slide 9 10.5 Example 3: ABC ~ DEF. Find the missing sides and missing angles. Since the triangles are similar, the corresponding angles are congruent. 82 A D A       34 C F F       Angles in a triangle add up to 180 180 82 34 180 64 A B C B B                Corresponding sides are proportional. Set up the proportion… 10.5 7 12 y  7 126y  18y  10.5 7 14 z  7 147z  21z 
  • 10. Slide 10 Example 4: Tom wants to find the height of a tall evergreen tree. He places a mirror on the ground and positions himself so that he can see the reflection of the top of the tree in the mirror. The mirror is 0.7 m away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall is the tree? Note: the triangles are similar.
  • 11. Set up the proportion and solve… Slide 11 Example 4: Tom wants to find the height of a tall evergreen tree. He places a mirror on the ground and positions himself so that he can see the reflection of the top of the tree in the mirror. The mirror is 0.7 m away from him and 5.5 m from the tree. If Tom is 1.8 m tall, how tall is the tree? Note: the triangles are similar. Answer: The tree would be 14.14 m tall. 1.8 0.7 5.5h  0.7 9.9h  0.7 0.7 9 .7 .9 0 h  14.14h 