MathGrade 8ages 13–14
🔺 Similarity
Two triangles are similar when they have the same angles but different sizes — a distinction that gets lost when "similar" sounds close enough to "the same."
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- In similar triangles all the angles are equal.
- Every side grows by the same multiplier, which is why the shape does not distort.
- If only some sides grow, the angles shift and the shape is no longer similar.
- Congruent shapes are similar with a multiplier of one, that is, at the same size too.
The mistake most kids make here
Thinking similar means identical.
Try one question
In similar triangles, what is necessarily equal?
What is equal
- the angles
- the sides
- the area
Answer
the angles — That's it. The sides grow, the angles stay put.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say what is kept and what changes between similar triangles.
How to help at home
The word "similar" in everyday speech means "kind of alike." In geometry it means something exact: same angles, sides scaled by the same number. That gap between the everyday word and the math word is where the confusion lives.
Print or draw the same triangle at two sizes (a phone photo enlarged and shrunk works too). Ask your child to measure the angles in each with a protractor, or just compare them by eye at the corners. Same angles, different side lengths — that's similarity.
When your child says two shapes are similar because they "look alike," ask: "if I only stretched the top side and left the others the same, would it still be the same shape?" Guide them to see that stretching just one part changes the angles too.
A sign they've got it: given two triangles, they check the angles first, not just a general impression of shape, before deciding whether they're similar.
Questions parents ask
- What's the difference between similar and congruent shapes?
- Similar shapes have the same angles and proportional sides; congruent shapes are similar with the scaling factor equal to one, meaning they're also the same size.
- How can I check if two triangles are similar without a protractor?
- Compare the ratios of corresponding sides. If every pair of matching sides has the same ratio to each other, the triangles are similar even without measuring angles directly.
- Why do the angles matter more than the sides for similarity?
- The angles decide the shape's proportions. Once the angles match, scaling every side by the same number keeps those proportions, which is exactly what similarity means.
- How does Maya teach similarity?
- Maya has the child compare angles first and sides second, so similarity is built from what stays fixed rather than from a vague sense of looking alike.
No card needed. The first lesson is free.
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