Maths : Rules of Congruence and 20 Questions

Congruence (Classes 6–10)

Meaning of Congruence

Two figures are congruent if they have the same shape and the same size.

Symbol used: ≅

If △ABC ≅ △DEF, then:

• AB = DE
• BC = EF
• AC = DF
• Corresponding angles are equal

Rules (Criteria) of Congruence

1. SSS (Side–Side–Side)

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

2. SAS (Side–Angle–Side)

If two sides and the included angle are equal, then triangles are congruent.

3. ASA (Angle–Side–Angle)

If two angles and the included side are equal, then triangles are congruent.

4. AAS (Angle–Angle–Side)

If two angles and one corresponding side are equal, then triangles are congruent.

5. RHS (Right angle–Hypotenuse–Side)

In right-angled triangles, if the hypotenuse and one side are equal, then triangles are congruent.

20 Questions with Step-by-Step Answers

Q1.

Triangles with sides 5 cm, 6 cm, 7 cm and 5 cm, 6 cm, 7 cm.

All three sides are equal.
Rule: SSS
✔ Triangles are congruent.

Q2.

AB = DE, BC = EF, ∠B = ∠E.

Two sides and included angle are equal.
Rule: SAS
✔ Congruent.

Q3.

Angles 40°, 60° and included side 5 cm.

Two angles and included side equal.
Rule: ASA
✔ Congruent.

Q4.

Is AAA a congruence rule?

AAA gives similarity only.
❌ Not a congruence rule.

Q5.

Right triangles: hypotenuse 10 cm, side 6 cm.

Right angle + hypotenuse + side equal.
Rule: RHS
✔ Congruent.

Q6.

All angles and one side equal.

Rule: AAS

Q7.

If △ABC ≅ △PQR, write corresponding sides.

AB = PQ
BC = QR
AC = PR

Q8.

Sides 3,4,5 and 3,4,6.

All three sides not equal.
❌ Not congruent.

Q9.

Rule used only for right triangles?

RHS Rule

Q10.

∠A = ∠D, ∠B = ∠E, AC = DF.

Two angles and one side equal.
Rule: AAS

Q11.

AB = XY, BC = YZ, ∠B = ∠Y.

Two sides and included angle equal.
Rule: SAS

Q12.

Two equilateral triangles of side 6 cm.

All sides equal.
Rule: SSS
✔ Congruent.

Q13.

Why RHS different from SAS?

RHS applies only to right triangles.

Q14.

If corresponding parts are equal?

Triangles are congruent.

Q15.

One side, right angle, hypotenuse equal.

RHS Rule

Q16.

Same area but different shapes?

❌ Not congruent.

Q17.

Are perimeters equal for congruent triangles?

✔ Yes, corresponding sides equal.

Q18.

Rule needing exactly three equal measurements?

SSS Rule

Q19.

Congruent triangles are always similar?

✔ True

Q20.

Symbol for congruence?

≅