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CBSE Class 7 · Mathematics

Geometric Twins

Official NCERT chapter from Ganita Prakash Part II (book code gegp2). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Geometric Twins” in Ganita Prakash Part II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 7
  • Easy level
  • 8 concepts

1Geometric Twins

Geometric twins are figures that match by a correspondence: same size, same shape, one can sit on the other. Congruence is the school word for that match.

Similar-looking is not a twin until sides and angles match under a pairing.

Figure. Geometric twins match in shape and size — they can sit on each other. A larger copy can look similar and still fail the twin test. Same angles without the same sides is not congruence.

How it works

  1. Name a pairing of verticesA↔P, B↔Q, C↔R.
  2. Check the matched sides and anglesThe twin-test.
  3. If they all match, call them congruentTwins.

2Congruence of Triangles

Two triangles are congruent if a named rule holds: SSS, SAS, ASA, RHS (right-hypotenuse-side) as taught. The rule is a sufficient test — you do not measure every leftover if the rule is met.

AAA is not a congruence rule here — that can be the same shape at a different size.

Figure. SSS congruence: three pairs of matching sides (here 7, 6, 5) force the triangles to be twins. Name vertices in matching order — ABC to DEF — before chasing an angle.

How it works

  1. Pick a rule you were taughtSSS, SAS, ASA, or RHS.
  2. See those parts match under a pairingThe given.
  3. Claim congruence by that ruleName the rule.

3Angles of Isosceles and Equilateral Triangles

In an isosceles triangle the base angles match. In an equilateral triangle all three angles are 60°. Those are angle-jobs that follow from equal sides.

Assuming 60° in a two-tick isosceles is a steal from equilateral.

Figure. Isosceles: the two marked legs are equal, so the two base angles are equal. Equilateral: all three sides equal, so each angle is 60°. The right triangle is drawn equilateral; the left is not.

How it works

  1. See two equal sidesIsosceles.
  2. Mark the two base angles equalThe job.
  3. Only if three sides equal, take 60° eachEquilateral.

4A definition is a test you can run

Congruence is a test: a pairing plus a rule. A definition you cannot pair is a poster of “same”.

Two drawings both labelled ABC are not automatically twins.

Figure. A geometry sentence is a drawing plus named facts. Until equal lengths and the right angle are inked, you are staring. The next mark is the claim those facts force — not a tidy look.

How it works

  1. Write the pairingThe definition’s object.
  2. Run SSS / SAS / ASA / RHS if that is the lessonThe test.
  3. If no pairing, you do not yet have twinsName vertices.

5Name the given before the unknown

The given are the matching marks (ticks, arcs, a right-box). The unknown is whether the triangles are congruent, or a leftover equal part. Read the marks first.

Granting SAS when only two sides are marked is a silent given.

Figure. Name the given sides first. Here the two legs are given; the base and its angles are the unknown. Asking for BC before locking AB and AC is the usual miss.

How it works

  1. Copy the marksThe given.
  2. Name the questionCongruent? A missing length?
  3. Apply only a rule the marks supportGiven first.

6One worked case is enough at this class

One paired pair of triangles is enough. A page of the same SSS clone does not add a new rule.

Ten twins of the same diagram are still one case.

Figure. One worked SSS case is enough at this class: sides 7, 6, 5 on both triangles. If three sides match, the twin is forced — you do not need a second different triangle to believe the test.

How it works

  1. Run one rule on one pairThe case.
  2. A second pair only if the rule changesA check.
  3. StopThis class.

7A miss: swapping the school name for the picture

Twin leaves or twin windows are a setting. The maths is the marked triangles. Measuring the leaf and skipping the pairing is the swap-miss.

Two similar photographs are not SSS.

Figure. A miss: swapping the school name for the picture. Two drawings that look tidy are not twins until correspondence is named. △ABC ≅ △DEF is a test; a pretty pair is not.

How it works

  1. Keep the photo as a storyLeaves, windows.
  2. Mark the triangles and the pairingThe maths.
  3. Run the rule on the marksDo not swap.

8Check by the opposite action or the opposite test

Check a congruence claim by asking which rule you used. If you cannot name SSS/SAS/ASA/RHS, the claim is a look. Try to break it with one unmatched part.

“They look the same” is not the opposite test.

Figure. The opposite test of a congruence claim is CPCT: if △ABC ≅ △DEF, then AB = DE, BC = EF, CA = FD. If a corresponding pair fails, the claim was wrong — do not keep the pretty drawing.

How it works

  1. Name the ruleThe claim’s reason.
  2. Hunt one unmatched needed partThe check.
  3. If you find one, mend or drop the claimHonest.
AAA at this class
  1. Does not prove congruence — size can differ
  2. Is SSS
  3. Is enough for twins

Same shape is not the same size.

Notes

  • The official chapter title is “Geometric Twins”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Recap

Hold these pegs from the official chapter “Geometric Twins”. The wording is ExamMaster’s teaching, not a textbook recap.

Geometric Twins
Geometric twins are figures that match by a correspondence: same size, same shape, one can sit on the other.
Congruence of Triangles
Two triangles are congruent if a named rule holds: SSS, SAS, ASA, RHS (right-hypotenuse-side) as taught.
Angles of Isosceles and Equilateral Triangles
In an isosceles triangle the base angles match.
A definition is a test you can run
Congruence is a test: a pairing plus a rule.
Name the given before the unknown
The given are the matching marks (ticks, arcs, a right-box).
One worked case is enough at this class
One paired pair of triangles is enough. A page of the same SSS clone does not add a new rule.

Practise Geometric Twins

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  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
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