Class 7 Mathematics

Chapter 7: Congruence of Triangles

STAGE 0: Foundation

Two figures are said to be congruent if they have the same shape and the same size. When two triangles are congruent, they fit exactly over each other.

Examples in daily life:

• Two identical keys
• Two equal coins
• Two identical tiles

STAGE 1: Congruent Triangles

If two triangles have:

• Equal corresponding sides
• Equal corresponding angles

then the triangles are congruent.

Notation:
△ABC ≅ △PQR

STAGE 2: SSS Congruence Rule

SSS (Side–Side–Side): If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Example:
If AB = PQ, BC = QR, CA = RP, then △ABC ≅ △PQR.

STAGE 3: SAS Congruence Rule

SAS (Side–Angle–Side): 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:
AB = PQ, ∠B = ∠Q, BC = QR ⇒ △ABC ≅ △PQR.

STAGE 4: ASA Congruence Rule

ASA (Angle–Side–Angle): 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.

STAGE 5: RHS Congruence Rule

RHS (Right angle–Hypotenuse–Side): This rule applies only to right-angled triangles.

• Right angle is equal
• Hypotenuse is equal
• One side is equal

Then the triangles are congruent.

STAGE 6: Practice Questions

1. What does congruent mean?
2. Name any two congruence rules.
3. Which rule is used for right-angled triangles?
4. Are two triangles with equal sides always congruent?
5. Write the full form of SAS.

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Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 7: Congruence of Triangles

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