Similar Figures.pdf - Kuta Software - Free Printable

Since both ExplainAnswer and TeachTopic are false, we will skip those sections entirely.

We’ll solve each of the 8 problems step by step using proportions from similar figures — meaning corresponding sides are in proportion.

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Problem 1:
Left triangle: sides 12, 20
Right triangle: sides 9, x
Set up proportion:
12 / 9 = 20 / x
Cross multiply: 12x = 180 → x = 15

✔ Check: 12/9 = 4/3; 20/15 = 4/3 → Correct.

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Problem 2:
Left triangle: sides x, 1
Right triangle: sides 6, 3
Proportion: x / 6 = 1 / 3
Cross multiply: 3x = 6 → x = 2

✔ Check: 2/6 = 1/3 → Correct.

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Problem 3:
Left triangle: sides x, 4
Right triangle: sides 8, 10
Proportion: x / 8 = 4 / 10
Cross multiply: 10x = 32 → x = 3.2

✔ Check: 3.2/8 = 0.4; 4/10 = 0.4 → Correct.

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Problem 4:
Left triangle: sides 5, 4
Right triangle: sides x, 8
Proportion: 5 / x = 4 / 8 → simplify 4/8 to 1/2
So 5/x = 1/2 → x = 10

✔ Check: 5/10 = 1/2; 4/8 = 1/2 → Correct.

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Problem 5:
Left triangle: sides 14, x
Right triangle: sides 2, 1
Proportion: 14 / 2 = x / 1 → 7 = x → x = 7

✔ Check: 14/2 = 7; 7/1 = 7 → Correct.

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Problem 6:
Left triangle: sides ?, 9 (base), top side is labeled “?” but actually looking at diagram: left has base 9, right side 6? Wait — let’s re-read.

Actually, problem 6 shows two triangles:

Left: base = 9, one side = 6
Right: base = x, corresponding side = 24

Assuming the 6 corresponds to 24, and 9 corresponds to x.

Proportion: 6 / 24 = 9 / x → simplify 6/24 = 1/4
So 1/4 = 9/x → x = 36

✔ Check: 6/24 = 1/4; 9/36 = 1/4 → Correct.

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Problem 7:
Left triangle: sides 9, 10
Right triangle: sides x, 60
Proportion: 9 / x = 10 / 60 → simplify 10/60 = 1/6
So 9/x = 1/6 → x = 54

✔ Check: 9/54 = 1/6; 10/60 = 1/6 → Correct.

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Problem 8:
Left triangle: sides 10, 10
Right triangle: sides x, 100
Proportion: 10 / x = 10 / 100 → simplify 10/100 = 1/10
So 10/x = 1/10 → x = 100

Wait — that would mean x=100? But then both triangles have same shape? Let’s check correspondence.

Actually, if left has two sides 10 and 10 (isosceles), and right has one side 100 and missing side x, and they’re similar, then ratio is 10:100 = 1:10.

So the other side should also be scaled by 10 → x = 10 * 10 = 100.

But wait — maybe the 10 on left corresponds to 100 on right, so scale factor is 10. Then the other 10 becomes 100. So x = 100.

✔ Check: 10/100 = 1/10; 10/100 = 1/10 → Correct.

BUT — looking again at problem 8: left triangle has sides 10 and 10, right has 100 and x. If it's similar, and assuming the 10 corresponds to 100, then x must correspond to the other 10 → x = 100.

Yes.

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Final Answers for all 8:

1) 15
2) 2
3) 3.2
4) 10
5) 7
6) 36
7) 54
8) 100

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Final Answer:
1) 15
2) 2
3) 3.2
4) 10
5) 7
6) 36
7) 54
8) 100