Finding missing sides of similar figures worksheet answers

Q: How do you find similar sides?

If two objects have the same shape, they are called similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.

Use the diagram shown below to answer the problems given below.

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Detailed Answer Key
How do you find missing angles in similar figures?
How do you find similar sides?

Problem 1 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 9, n = 6, o = 8, p = 4

Problem 2 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 24, l = 30, m = 15, n = 16

Problem 3 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

m = 11, p = 6, n = 5, o = 4

Problem 4 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 16, l = 13, m = 12, o = 7

Detailed Answer Key

Problem 1 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 9, n = 6, o = 8, p = 4

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

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

m = 6

l/8 = 9/6

l = 9(8) / 6

l = 72/6

l = 12

So, the missing sides of the triangle KLM are 6 and 12.

Problem 2 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 24, l = 30, m = 15, n = 16

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

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

p = 10

30/o = 24/16

o = 30(16) / 24

o = 480/24

o = 20

So, the missing sides of the triangle KLM are 10 and 20.

Problem 3 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

m = 11, p = 6, n = 5, o = 4

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

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

k = 9.16

l/4 = 11/6

l = 11(4) / 6

l = 44/6

l = 7.33

So, the missing sides of the triangle KLM are 9.16 and 7.33.

Problem 4 :

Find the measures of the missing sides if ΔKLM ∼ ΔNOP.

k = 16, l = 13, m = 12, o = 7

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

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

p = 6.46

16/n = 13/7

n = 16(7) / 13

l = 44/6

l = 8.61

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How do you find missing angles in similar figures?

Steps for Finding Missing Angles in Similar Triangles Step 1: Identify corresponding angles in the similar triangles. Step 2: Find the missing measurements of the congruent angles. Step 3: Using the fact that all the angles in a triangle must sum to 180∘ , find the final missing angle in one of the two triangles.

How do you find similar sides?

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.