Shapes that fit over each other exactly
Geometric twins
Cut two triangles from one template, lay one on the other, and it disappears underneath.
📚 Chapter Learning Kit
Geometric Twins · Class 7 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
⚡ Veda Bites
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Not how they look side by side
The test is covering
Two shapes seen side by side can easily mislead the eye.
Which way it lies does not matter
Turning and flipping are allowed
The second shape may need turning, or even flipping over, before it fits.
Three well-chosen measurements do it
You need not check all six
Two triangles have six measurements each, three sides and three angles.
The SSS criterion
Three sides are enough
Give the three sides as 5 cm, 6 cm and 9 cm, and only one triangle fits.
The two arcs cross in one place
Why three sides settle it
Draw the longest side, then sweep an arc from each end with the other two lengths.
📖 Smart notes
What you'll study, topic by topic
1
Congruence, and saying which corner matches which
Congruent shapes fit over each other exactly, after any turning or flipping needed. The same shape alone is not enough, and the same size alone is not enough either. A congruence statement carries a correspondence in the…
- Congruent shapes fit over each other with no gap and nothing sticking out.
- Turning and flipping the second shape are both allowed.
- Two triangles of one shape at different sizes are not congruent.
~35 min · full explanation, examples & memory tricks in the app
2
The four criteria, and the two that are not
Three well-chosen measurements prove congruence, and four criteria do the work: SSS, SAS, ASA and RHS. Each names at least one side, because angles alone fix only the shape. Three angles leave the size open, and two side…
- Three well-chosen measurements are usually enough to prove congruence.
- SSS gives one triangle because the two swept arcs cross in one place.
- SAS needs the angle BETWEEN the two given sides.
~45 min · full explanation, examples & memory tricks in the app
3
Isosceles and equilateral angles, proved by a fold
Folding an isosceles triangle makes two halves congruent by SSS, which proves the base angles equal. From the apex the base angles follow, and from a base angle the apex follows. Every equilateral triangle has 60 degree…
- The apex of an isosceles triangle sits between its two equal sides.
- Folding one equal side onto the other creases from the apex to the base.
- The two halves have three pairs of equal sides, so SSS makes them congruent.
~40 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Two shapes are laid one on top of the other and neither leaves a gap nor sticks out anywhere. Shapes that fit like that are called
Beginner
A similar
B equal in area
C congruent
D parallel
Show answer & explanation
congruent
They are geometric twins.
Two shapes are to be tested, and only one test settles the matter whatever they look like side by side. The real test is whether one can be
Beginner
A drawn beside the other
B laid over the other exactly
C measured as the other
D folded in half
Show answer & explanation
laid over the other exactly
With no gap and nothing sticking out.
When testing congruence, turning the second shape is
Intermediate
A not allowed at all
B allowed, and so is flipping
C allowed, but flipping is not
D allowed only for triangles
Show answer & explanation
allowed, and so is flipping
Position does not matter.
Two triangles have exactly the same shape but one of them has been drawn larger than the other. Such a pair is
Intermediate
A congruent
B not congruent
C congruent if turned
D congruent if flipped
Show answer & explanation
not congruent
One is simply bigger than the other.
🃏 Flashcards
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Fact Or Myth
Sequence Builder
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