Geometric Twins — Class 7 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Geometric Twins" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Geometric Twins" — 8 important questions with detailed answers for CBSE board exam…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

What does SSS congruence criterion mean? Give an example.
Two triangles have two sides and the included angle equal. What is this congr…
Explain ASA congruence criterion and state the difference between ASA and AAS.
What is RHS congruence criterion? Can it be applied to acute-angled triangles?
Triangle ABC has AB = 5 cm, BC = 7 cm, CA = 8 cm. Triangle DEF has DE = 5 cm,…
In triangles MNO and PQR, MN = PQ, NO = QR, and angle N = angle Q. Are these …
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
What does SSS congruence criterion mean? Give an example.	✓ Solved
Two triangles have two sides and the included angle equal…	✓ Solved
Explain ASA congruence criterion and state the difference…	✓ Solved
What is RHS congruence criterion? Can it be applied to ac…	✓ Solved
Triangle ABC has AB = 5 cm, BC = 7 cm, CA = 8 cm. Triangl…	✓ Solved
In triangles MNO and PQR, MN = PQ, NO = QR, and angle N =…	✓ Solved

Showing 6 of 8 questions

Q1: What does SSS congruence criterion mean? Give an example.

SSS (Side-Side-Side) congruence criterion states that if all three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent. Example: Triangle ABC with sides AB = 5 cm, BC = 6 cm, CA = 7 cm Triangle PQR with sides PQ = 5 cm, QR = 6 cm, RP = 7 cm Since all three pairs of corresponding sides are equal, triangle ABC ≅ triangle PQR by SSS criterion.

Q2: Two triangles have two sides and the included angle equal. What is this congruence criterion called?

This is the SAS (Side-Angle-Side) congruence criterion. Definition: If two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle, then the triangles are congruent. Example: In triangle ABC and triangle DEF: AB = DE = 4 cm Angle ABC = Angle DEF = 60° BC = EF = 5 cm Then triangle ABC ≅ triangle DEF by SAS criterion. Note: The angle must be between the two equal sides (included angle).

Q3: Explain ASA congruence criterion and state the difference between ASA and AAS.

ASA (Angle-Side-Angle) Criterion: If two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the triangles are congruent. Example: In triangle PQR and triangle XYZ: Angle P = Angle X = 50° PQ = XY = 6 cm (included side) Angle Q = Angle Y = 70° Then triangle PQR ≅ triangle XYZ by ASA criterion. Difference between ASA and AAS: ASA: Two angles and the included side (side between the angles) are equal. AAS: Two angles a...

Q4: What is RHS congruence criterion? Can it be applied to acute-angled triangles?

RHS (Right angle-Hypotenuse-Side) Congruence Criterion: This criterion applies ONLY to right-angled triangles. Definition: If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then the two right-angled triangles are congruent. Example: In right triangle ABC (right angle at B) and right triangle PQR (right angle at Q): AC = PR = 10 cm (hypotenuses) AB = PQ = 6 cm (one side) Then triangle ABC ≅ triangle...

Q5: Triangle ABC has AB = 5 cm, BC = 7 cm, CA = 8 cm. Triangle DEF has DE = 5 cm, EF = 7 cm, FD = 8 cm. Prove the triangles are congruent and write the congruence statement.

Step 1: Compare the corresponding sides AB = 5 cm and DE = 5 cm → AB = DE ✓ BC = 7 cm and EF = 7 cm → BC = EF ✓ CA = 8 cm and FD = 8 cm → CA = FD ✓ Step 2: Check which criterion applies All three pairs of corresponding sides are equal. This satisfies the SSS (Side-Side-Side) congruence criterion. Step 3: Write the congruence statement Triangle ABC ≅ Triangle DEF (by SSS criterion) Note: The order of vertices in the congruence statement matters. It shows the correspondence: A ↔ D, B ↔ E, C ↔ F

Q6: In triangles MNO and PQR, MN = PQ, NO = QR, and angle N = angle Q. Are these triangles congruent? If yes, by which criterion?

Step 1: Identify the given information MN = PQ (one pair of sides equal) NO = QR (another pair of sides equal) Angle N = Angle Q (angles equal) Step 2: Check if angle is included Angle N is between sides MN and NO. Angle Q is between sides PQ and QR. Yes, the angle is between the two given sides (included angle). Step 3: Apply congruence criterion Two sides (MN and NO) and the included angle (angle N) are equal to the corresponding two sides (PQ and QR) and included angle (angle Q). Conclusio...

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