Similarity Theorem SSS (Side-Side-Side)

Similarity Theorem SSS (Side-Side-Side). Practice questions to deepen understanding of the SSS similarity theorem (Side-Side-Side). Online math practice with full solutions and step-by-step explanations.

SSS similarity practice — the Side-Side-Side similarity theorem, checking ratios and identifying similar triangles. Detailed explanations.

25 questions

Question 1

4.00 pts

📐 SSS similarity theorem:
two similar triangles :

three sides of one triangle proportional to three sides of the other

two sides equal

three sides equal

two sides proportional

Explanation:

💡 :

1: SSS similarity theorem 🔍

side-side-side ✨

3 sides one

proportional

3 sides two

Question 2

4.00 pts

✓ identification :
ABC: sides 6, 8, 10
DEF: sides 3, 4, 5
similar by SSS similarity?

Yes - ratio 2:1

No - sides

No - angles

Yes - because Pythagorean theorem

Explanation:

💡 :

1: 🔍

ABC:
🔹 sides: 6, 8, 10

DEF:
🔹 sides: 3, 4, 5

2: ratio 📐

ratio :
6/3 = 2

Question 3
4.00 pts

🔢 ratio:
ABC: sides 5, 7, 9
DEF: sides 10, 14, 18
similarity ratio ABC:DEF?

1:2

2:1

1:3

5:10

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 5, 7, 9

DEF:
🔹 sides: 10, 14, 18
2: ratio 📐
10/5 = 2

Question 4
4.00 pts

⚠️ identification :
ABC: sides 3, 4, 5
DEF: sides 6, 8, 11
?

No - ratio different (5:11≠3:6)

Yes - two sides proportional

Yes - ratio 1:2

insufficient data

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 3, 4, 5

DEF:
🔹 sides: 6, 8, 11
2: ratio 📐
ratio :
6/3 = 2

Question 5
4.00 pts

🤔 three?
because according to SSS similarity
two sides proportional?

No - three sides

Yes - two

depends on the triangle

Yes - ratio equal

Explanation:

💡 :
1: three? 🔍
SSS similarity theorem ✨
three sides

No two!
2: 📊

Question 6
4.00 pts

🎯 :
ABC: sides 4, 6, 8
DEF: sides 6, 9, x
similar triangles. x?

12

10

11

14

Explanation:

💡 :
1: 🔍

given:
🔹 ABC: 4, 6, 8
🔹 DEF: 6, 9, x
🔹 similar triangles
2: similarity ratio 📐
sides :

6/4 =

Question 7
4.00 pts

🔄 :
ABC: sides AB=3, BC=4, CA=5
DEF: sides DE=9, EF=12, FD=15
?

ABC ~ DEF

ABC ~ DFE

ABC ~ EDF

No

Explanation:

💡 :
1: identification sides 🔍
ABC:
🔹 AB = 3
🔹 BC = 4
🔹 CA = 5

DEF:
🔹 DE = 9
🔹 EF = 12
🔹 FD = 15
2: ratio 📐

Question 8
4.00 pts

🔢 :
ABC: sides 6, 9, 12
DEF: sides 4, 6, 8
similarity ratio No ?

3:2

2:3

6:4

1:2

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 6, 9, 12

DEF:
🔹 sides: 4, 6, 8
2: ratio 📐
ABC : DEF

= 6:4

= 9:6

= 12:8

Question 9
4.00 pts

🔢 :
ABC: sides 2.5, 3, 4
DEF: sides 5, 6, 8
?

Yes - ratio 1:2

No - No

No - ratio

insufficient data

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 2.5, 3, 4

DEF:
🔹 sides: 5, 6, 8
2: ratio 📐
5/2.5 = 2

Question 10
4.00 pts

🔄 :
ABC: sides 5, 7, 9
DEF: sides 5, 7, 9
similarity ratio?

1:1 ()

No

2:1

ratio

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 5, 7, 9

DEF:
🔹 sides: 5, 7, 9
2: ratio 📐
5/5 = 1

Question 11
4.00 pts

🎯 two :
ABC: sides 4, x, 8
DEF: sides 6, 9, y
similar triangles. find x -y.

x=6, y=12

x=8, y=10

x=5, y=10

x=7, y=11

Explanation:

💡 :
1: 🔍
given:
🔹 ABC: 4, x, 8
🔹 DEF: 6, 9, y
🔹 similar triangles
2: similarity ratio 📐
side different:

6/4 =

Question 12
4.00 pts

⚠️ Finding the error:
A student claimed: "Triangles with sides 2,3,4 and 4,6,7 are similar because 4/2=2 and 6/3=2."
What is the error?

He forgot to check the third ratio (7/4 ≠ 2)

There is no error

Angles must be checked

The first ratio is wrong

Explanation:

💡 Detailed explanation:
For SSS similarity, all three ratios of corresponding sides must be equal.
4/2 = 2 and 6/3 = 2, but 7/4 = 1.75, not 2.
Therefore the third ratio breaks the similarity.

Question 13
4.00 pts

🔺 isosceles:
ABC isosceles: 5, 5, 6
DEF isosceles: 10, 10, 12
similar by SSS similarity?

Yes - ratio 1:2

No - "

angles

equal

Explanation:

💡 :
1: 🔍
ABC:
🔹 isosceles: 5, 5, 6

DEF:
🔹 isosceles: 10, 10, 12
2: ratio 📐
10/5 = 2

Question 14
4.00 pts

🔢 larger:
ABC: sides 15, 20, 25
DEF: sides 30, 40, 50
similarity ratio?

1:2

2:1

3:5

15:30

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 15, 20, 25

DEF:
🔹 sides: 30, 40, 50
2: ratio 📐
30/15 = 2

Question 15
4.00 pts

🔍 :
ABC: sides 3, 5, 7
DEF: sides 6, 10, 13
?

No - ratio different (13/7≠2)

Yes - ratio 1:2

Yes - two sides proportional

insufficient data

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 3, 5, 7

DEF:
🔹 sides: 6, 10, 13
2: ratio 📐
ratio :
6/3 = 2

Question 16
4.00 pts

🔢 :
ABC: sides 1.5, 2, 2.5
DEF: sides 3, 4, 5
similarity ratio?

1:2

2:1

3:5

1.5:3

Explanation:

💡 :
1: 🔍
ABC:
🔹 sides: 1.5, 2, 2.5

DEF:
🔹 sides: 3, 4, 5
2: ratio 📐
3/1.5 = 2

Question 17
4.00 pts

📖 Problem:
The sides of a triangle are 6, 8, and 10 cm.
A similar triangle is built so that its smallest side is 9 cm.
What are the other sides?

12 cm and 15 cm

10 cm and 12 cm

11 cm and 13 cm

13 cm and 16 cm

Explanation:

💡 Detailed explanation:
The original smallest side is 6 cm, and the new smallest side is 9 cm.
The similarity ratio is 9/6 = 3/2.
8 · 3/2 = 12 and 10 · 3/2 = 15.
So the other sides are 12 cm and 15 cm.

Question 18
4.00 pts

📐 Pythagorean theorem:
sides 3k, 4k, 5k
(k ) ?

Yes - ratio always

No - -k

only if k=1

No -

Explanation:

💡 :
1: definition 🔍
✨
sides:

3k, 4k, 5k

(k = )
2: 📐

Question 19
4.00 pts

🔍 side:
ABC: sides 4, 5, x
DEF: sides 8, 10, 14
similar triangles. x?

7

6

8

12

Explanation:

💡 :
1: 🔍

given:
🔹 ABC: 4, 5, x
🔹 DEF: 8, 10, 14
🔹 similar triangles
2: similarity ratio 📐
sides known:

8/4 =

Question 20
4.00 pts

⚖️ theorem:
hypotenuse AA similarity theorem SSS similarity theorem?

AA similarity No sides

SSS similarity

AA similarity always Correct

no difference

Explanation:

💡 :
1: theorem 🔍
two theorem ✨
2: 📊

Question 21
4.00 pts

📦 rectangle:
rectangle 6×8 diagonal.
rectangle 9×12 diagonal.
?

Yes - ratio 2:3 sides

No -

diagonal

square

Explanation:

💡 :
1: 🔍
rectangle 1: 6×8
🔹 sides: 6, 8
🔹 diagonal: ?

rectangle 2: 9×12
🔹 sides: 9, 12
🔹 diagonal: ?
2: diagonals 📐

Question 22
4.00 pts

🔄 :
ABC: sides x, 6, 9
DEF: sides 12, 18, 27
similar triangles. x?

4

3

5

8

Explanation:

💡 :
1: 🔍
ABC (small):
🔹 sides: x, 6, 9

DEF (large/greater):
🔹 sides: 12, 18, 27
2: similarity ratio 📐
sides known:

Question 23
4.00 pts

📖 :
perimeter 24 cm
perimeter 36 cm.
side small 6 cm,
side larger?

9 cm

8 cm

10 cm

12 cm

Explanation:

💡 :
1: 🔍
small:
🔹 perimeter: 24 cm
🔹 side one: 6 cm

large/greater:
🔹 perimeter: 36 cm
🔹 side : ?
2: ratio of perimeters 📐

Question 24
4.00 pts

⚠️ Common mistake:
A student said: "If 6/3=2 and 8/4=2, then the triangles are similar."
What is missing?

Checking the third ratio

Checking angles

Calculating area

Nothing — it is correct

Explanation:

💡 Detailed explanation:
SSS similarity requires checking three pairs of corresponding sides.
Two equal ratios are not enough. The third side ratio must also be equal.

Question 25
4.00 pts

🌟 summary SSS similarity theorem:
?

three proportional sides prove

two sides proportional

angles equal

only congruent triangles are similar

Explanation:

💡 :
1: SSS similarity theorem 🔍
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side-side-side ✨
3 sides
proportional
( ratio)

↓