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Geometric Twins – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 9. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Congruent figures are exact copies — same shape and same size. Triangles are congruent if certain sides and angles match.

Congruence

Congruent figures fit exactly on each other (symbol ≅).
Corresponding parts of congruent triangles are equal (CPCT).
Line segments are congruent if they have the same length; angles if they have the same measure.

Criteria for triangles

SSS: three sides equal.
SAS: two sides and the included angle equal.
ASA: two angles and the included side equal.
RHS: right angle, hypotenuse and one side equal.

Key terms

Congruent: same shape and same size
CPCT: corresponding parts of congruent triangles are equal
Included angle: angle between two given sides

Formulas

≅ means "is congruent to"

Important questions with answers

If △ABC ≅ △PQR, write the corresponding parts.2 marks

A ↔ P, B ↔ Q, C ↔ R; AB = PQ, BC = QR, CA = RP, and ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R.

Why is AAA not a congruence rule?3 marks

Two triangles can have the same three angles but different sizes (one an enlargement of the other). They are similar, not congruent.

In △ABC and △DEF, AB = DE = 5 cm, ∠B = ∠E = 60°, BC = EF = 7 cm. Are they congruent? Name the rule, write the correspondence and two more equal parts by CPCT.5 marks

Yes, by SAS (two sides and the included angle are equal). Correspondence: A ↔ D, B ↔ E, C ↔ F, so △ABC ≅ △DEF. By CPCT: AC = DF, ∠A = ∠D (and ∠C = ∠F).

Quick revision

Four rules: SSS, SAS, ASA, RHS.
CPCT gives equal parts after proving congruence.
Congruent ⇒ equal area.

Exam tips

Write matching vertices in the same order: △ABC ≅ △PQR means A ↔ P.
AAA is not a congruence rule — it gives same shape, not same size.

Practice MCQs

Congruent figures have
1. same shape only
2. same shape and size
3. same size only
4. different shapes
Show answer
Answer: (b) same shape and size. Exact copies.
Two line segments are congruent if they have the same
1. colour
2. direction
3. length
4. position
Show answer
Answer: (c) length. Length.
Which is NOT a congruence criterion?
1. SSS
2. SAS
3. AAA
4. RHS
Show answer
Answer: (c) AAA. AAA only gives similarity.
In △ABC ≅ △PQR, AB corresponds to
1. PR
2. QR
3. RP
4. PQ
Show answer
Answer: (d) PQ. A ↔ P, B ↔ Q.
Two triangles with all three sides equal are congruent by
1. SAS
2. SSS
3. ASA
4. RHS
Show answer
Answer: (b) SSS. Side-side-side.
Two right triangles have equal hypotenuses and one equal side. They are congruent by
1. SAS
2. ASA
3. SSS only
4. RHS
Show answer
Answer: (d) RHS. RHS.
If △DEF ≅ △XYZ and ∠E = 65°, then
1. ∠X = 65°
2. ∠Z = 65°
3. ∠Y = 65°
4. cannot say
Show answer
Answer: (c) ∠Y = 65°. E ↔ Y.
Which condition does NOT guarantee congruence
1. SSS
2. SAS
3. AAA
4. ASA
Show answer
Answer: (c) AAA. Same angles, different sizes possible.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.