Similar Triangles
Match corresponding parts first, then apply one consistent scale factor.
Similar Triangles
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Similar triangles have equal corresponding angles and proportional sides
Similarity preserves shape, not size. Corresponding side lengths share one scale factor. Perimeters use that factor; areas use its square.
Length scale
larger side ÷ corresponding smaller side
Area scale
If lengths scale by k, areas scale by k².
Match first; calculate second
Problem: Two triangles are similar. A 6-cm side in the smaller triangle corresponds to 18 cm in the larger. What corresponds to a 5-cm side?
Recognize: The larger triangle is an enlargement of the smaller one. Since 6 cm became 18 cm, each corresponding side was multiplied by 3.
Do it fast: Scale factor = 18÷6=3. Apply that same factor to the matching 5-cm side: 5×3=15 cm.
Answer: 15 cm.
Before calculating, confirm that the sides correspond—usually by matching the equal angles opposite them.
Why it works
Similar triangles are one consistent enlargement or reduction. Once the correct scale factor is known, it applies to every corresponding length.
Five forms you should recognize
If a 3-cm side becomes 9 cm, divide 9÷3. The scale factor is k=3.
If the scale factor is 3, a corresponding 4-cm side in the smaller triangle becomes 4×3=12 cm in the larger triangle.
Perimeter 15 enlarged by 2 becomes 30.
Area 10 enlarged by 2 becomes 40.
Two equal angle pairs guarantee similarity.
Check before you commit
- Matching sides by visual position
- Reversing one ratio
- Adding the scale factor
- Using k instead of k² for area
- Assuming similar means congruent
- Trusting a diagram’s scale
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Similar Triangles FAQ
Why are there two mastery sets?
A different five-question set appears after an unsuccessful attempt so memorizing one set does not verify mastery.
Does 5/5 mean I never need this topic again?
It verifies this competency today; revisit it later through mixed practice.
Continue your mathematics review.
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