How to find the missing sides of similar triangles :
In geometry two triangles are similar if and only if corresponding angles are congruent and the lengths of corresponding sides are proportional.
Let us see some examples to understand how to find the missing sides of similar triangles.
Example 1 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 9, n = 6, o = 8, p = 4
Solution :
Since the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 9, n = 6, o = 8, p = 4
m/4 = 9/6 = l/8
m/4 = 9/6 m = 9(4) / 6 m = 36/6 ==> 6 |
l/8 = 9/6 l = 9(8) / 6 l = 72/6 ==> 12 |
Hence the missing sides of the triangle KLM are 6 and 12.
Example 2 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 24, l = 30, m = 15, n = 16
Solution :
Since the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 24, l = 30, m = 15, n = 16
15/p = 24/16 = 30/o
15/p = 24/16 p = 15(16) / 24 p = 240/24 ==> 10 |
30/o = 24/16 0 = 30(16) / 24 o = 480/24 ==> 20 |
Hence the missing sides of the triangle KLM are 10 and 20.
Example 3 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
m = 11, p = 6, n = 5, o = 4
Solution :
Since the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
m = 11, p = 6, n = 5, o = 4
11/6 = k/5 = l/4
11/6 = k/5 k = 11(5) / 6 k = 55/6 ==> 9.16 |
l/4 = 11/6 l = 11(4) / 6 l = 44/6 ==> 7.33 |
Hence the missing sides of the triangle KLM are 9.16 and 7.33.
Example 4 :
Find the measures of the missing sides if ΔKLM ∼ ΔNOP.
k = 16, l = 13, m = 12, o = 7
Solution :
Since the above triangles ΔKLM are ΔNOP similar, the ratios of the corresponding sides will be equal.
KL/NO = LM/OP = KM/NP
m/p = k/n = l/o
k = 16, l = 13, m = 12, o = 7
12/p = 16/n = 13/7
12/p = 13/7 p = 12(7) / 13 p = 84/13 ==> 6.46 |
16/n = 13/7 n = 16(7) / 13 l = 44/6 ==> 8.61 |
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