What similar means
Same shape, any size
Two figures are similar if they have the same shape, whether or not they are the same size.
↳ Angles stay put; lengths all scale together.
📚 Chapter Learning Kit
Triangles · Class 10 Mathematics
English 3 topics 171 leveled MCQs 60 flashcards 3 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
⚡ Veda Bites
💡 Key Idea
⚖️ Comparison
⭐ Important Fact
💡 Key Idea
➗ Formula
⚠️ Common Mistake
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The difference
Similar or congruent?
↳ Congruent is similar with scale factor 1.
Congruent ⟹ similar
One way only
ALL congruent figures are similar.
↳ This exact sentence is an exam favourite.
The Basic Proportionality Theorem
A parallel line splits both sides alike
If $DE \parallel BC$ in triangle $ABC$, then $\frac{AD}{DB} = \frac{AE}{EC}$.
↳ Also known as Thales' Theorem.
Part : part and part : whole
The two forms
↳ Choose one form and use it on both sides.
The commonest error here
Never mix the forms
$\frac{AD}{DB} = \frac{AE}{EC}$ ✓ and $\frac{AD}{AB} = \frac{AE}{AC}$ ✓
↳ Decide the form first, then write both sides.
📖 Smart notes
What you'll study, topic by topic
1
Similar Figures
Two figures are similar when they have the same SHAPE, whatever their size. For polygons that means two things at once: every pair of corresponding angles is equal, AND every pair of corresponding sides is in the same ra…
- Two figures are SIMILAR if they have the same shape, whether or not they have the same size.
- Two polygons with the same number of sides are similar if (i) their corresponding angles are equal AND (ii) their corresponding sides are in…
- BOTH conditions are needed for polygons — either one alone is not enough.
~35 min · full explanation, examples & memory tricks in the app
2
The Basic Proportionality Theorem
A line drawn parallel to one side of a triangle cuts the other two sides in the same ratio. This is the Basic Proportionality Theorem — the one theorem of this chapter you are asked to prove — and its converse runs the o…
- BPT (Theorem 6.1): if a line is drawn parallel to one side of a triangle to cut the other two sides in distinct points, those two sides are…
- In symbols: if $DE \parallel BC$ then $\frac{AD}{DB} = \frac{AE}{EC}$.
- It is also called Thales' Theorem.
~45 min · full explanation, examples & memory tricks in the app
3
Criteria for Similarity of Triangles
Triangles are far friendlier than other polygons: you never have to check both conditions. Equal angles alone force proportional sides (AA), proportional sides alone force equal angles (SSS), and one equal angle between…
- AAA: if corresponding angles of two triangles are equal, the triangles are similar.
- AA: two pairs of equal angles are enough, because the third pair then follows from the angle sum.
- SSS: if corresponding sides are in the same ratio, the triangles are similar.
~50 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
171 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Two figures are similar when they have
Beginner
A the same size, whatever their shape
B the same area
C the same shape, whatever their size
D the same perimeter
Show answer & explanation
the same shape, whatever their size
Similarity is about shape alone.
Two figures are congruent when they have
Beginner
A the same shape only
B the same shape and the same size
C the same size only
D equal areas
Show answer & explanation
the same shape and the same size
Congruence is the stricter idea.
Which statement is true?
Beginner
A all similar figures are congruent
B all congruent figures are similar
C no congruent figure is similar
D congruence and similarity are unrelated
Show answer & explanation
all congruent figures are similar
Congruence is similarity with scale factor 1; the converse fails.
The symbol $\sim$ means
Beginner
A is congruent to
B is equal to
C is similar to
D is parallel to
Show answer & explanation
is similar to
Congruence uses a different symbol.
🃏 Flashcards
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60 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
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