Pre-Algebra
Geometry
Congruence and similarity
20 practice questions
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Theory + worked examples
Congruence and Similarity
Texas Pre-Algebra (TEKS) • Standard 8.10(A) • Geometry
Congruence and Similarity is a topic in Geometry in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.10(A), which requires students to understand congruence and similarity of figures.
Congruent figures have the same shape and size; similar figures have the same shape with proportional sides.
Theory
Congruent figures have the same shape and size; similar figures have the same shape with sides in proportion.
Similar figures have equal angles and proportional sides.
Congruent and similar triangles.
The difference.
Similar sides:
\[\dfrac{\text{side}_1}{\text{side}_2}=\text{scale factor}\]
Congruent is similarity with scale factor \(1\).
How to compare figures
- Check if angles are equal.
- Compare corresponding side lengths.
- Equal sides: congruent.
- Proportional sides: similar.
Example 1 — Congruent?
Two triangles have identical side lengths. Congruent or similar?
Solution
Same size and shape — congruent.
Example 2 — Similar
A triangle is scaled by \(2\). Congruent or similar?
Solution
Same shape, bigger — similar.
Example 3 — Missing side
Similar triangles: sides \(3,4\) and \(6,x\). Find \(x\).
Solution
Proportional: scale \(2\).
| \(x\) | \(=\) | \(8\) |
Example 4 — Angles
What is true of angles in similar figures?
Solution
They are equal.
Common pitfalls
Similar is not congruent unless the scale factor is \(1\).
Similar figures have equal angles.
Match corresponding sides in the ratio.
Frequently asked questions
What does congruent mean?
Same shape and size.
What does similar mean?
Same shape, proportional sizes.
Are similar figures' angles equal?
Yes.
Is congruent a kind of similar?
Yes, with scale factor 1.
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