Similar Triangles Practice Worksheet

Practice solving similar triangle problems using proportions, scale factors, and missing side lengths.

Try each problem on your own first. Then click Show solution to check the proportion, scale factor, and final answer.

Similar Triangles Reminder

  • Similar triangles have the same shape but not necessarily the same size.
  • Corresponding angles are congruent.
  • Corresponding sides are proportional.
  • AA similarity is often enough to prove two triangles are similar.
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Level 1: Scale Factor

Problem 1

Two similar triangles have corresponding side lengths \(3\) and \(9\). What is the scale factor from the smaller triangle to the larger triangle?

Show solution

Divide the larger side by the smaller side.

\[ \frac{9}{3}=3 \]

The scale factor is \(3\).

Problem 2

A triangle has side lengths \(4, 6, 8\). A similar triangle is enlarged by a scale factor of \(2\). What are the new side lengths?

Show solution

Multiply each side length by \(2\).

\[ 4(2)=8,\quad 6(2)=12,\quad 8(2)=16 \]

The new side lengths are \(8, 12, 16\).

Problem 3

A larger triangle has a side of length \(20\). The scale factor from the smaller triangle to the larger triangle is \(4\). What is the corresponding side length in the smaller triangle?

Show solution

Divide by the scale factor.

\[ \frac{20}{4}=5 \]

The corresponding smaller side is \(5\).

Level 2: Proportions and Missing Sides

Problem 4

Two similar triangles have corresponding sides \(3\) and \(6\), and \(5\) and \(x\). Find \(x\).

\[ \frac{3}{6}=\frac{5}{x} \]
Show solution

Cross multiply.

\[ 3x=30 \] \[ x=10 \]

The missing side is \(10\).

Problem 5

Two similar triangles have corresponding sides \(4\) and \(10\), and \(6\) and \(x\). Find \(x\).

\[ \frac{4}{10}=\frac{6}{x} \]
Show solution

Cross multiply.

\[ 4x=60 \] \[ x=15 \]

The missing side is \(15\).

Problem 6

Two similar triangles have corresponding sides \(8\) and \(12\), and \(10\) and \(x\). Find \(x\).

\[ \frac{8}{12}=\frac{10}{x} \]
Show solution

Cross multiply.

\[ 8x=120 \] \[ x=15 \]

The missing side is \(15\).

Level 3: Similarity Reasoning

Problem 7

Two triangles have two pairs of corresponding angles congruent. What similarity rule proves the triangles are similar?

\[ \angle A \cong \angle D,\quad \angle B \cong \angle E \]
Show solution

Two pairs of congruent angles are enough to prove similarity.

\[ \triangle ABC \sim \triangle DEF \quad \text{by AA Similarity} \]
Problem 8

Are two triangles with side lengths \(3,4,5\) and \(6,8,10\) similar? Explain why.

Show solution

Compare corresponding side ratios.

\[ \frac{6}{3}=2,\quad \frac{8}{4}=2,\quad \frac{10}{5}=2 \]

Yes. All corresponding sides have the same scale factor, so the triangles are similar.

Need more help with similar triangles?

Similar triangles become easier when students carefully match corresponding sides before setting up proportions. For a full explanation, visit my Similar Triangles guide.

Related Geometry Resources

Similar Triangles Explained

Review scale factor, proportions, AA similarity, and corresponding sides.

Triangle Congruence

Compare similar triangles with congruent triangles and learn when triangles are exactly the same size.

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