Chapter 11 . Congruence of Triangles NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 11. CONGRUENCE OF TRIANGLES

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 11.1

1. In Δ ABC (Fig. 11.19) if ∠B = ∠C and AD ⊥ BC, then Δ ABD ≅ Δ ACD by the criterion.

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(a) RHS (b) ASA (c) SAS (d) SSS

Answer: (a) RHS

[ In ∆ADB and ∆ADC ,we have

AB=AC (∠B=∠C )

∠ADB=∠ADC=90°

AD=AD [ Common side]

∆ADB≅∆ADC [RHS] ]

2. In Fig. 11.20, ΔABC≅ΔPQR. This congruence may also be written as

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(a) Δ BAC ≅ Δ RPQ (b) Δ BAC ≅ Δ QPR (c) Δ BAC ≅ Δ RQP (d) Δ BAC ≅ Δ PRQ.

Answer: (b) ΔBAC≅ΔQPR

[ Since, ΔABC≅ΔPQR

AB=PQ , BC=QR , AC=PR

S0, ΔBAC≅ΔQPR (SSS) ]

3. In order that two given triangles are congruent, along with equality of two corresponding angles we must know the equality of :

(a) No corresponding side

(b) Minimum one corresponding side

(d) All the three corresponding sides

Answer: (b) Minimum one corresponding side.

[ For two triangles to be congruent, if two corresponding angles are equal, the third angle is also equal (Angle-Angle-Angle similarity). ]

4. Two triangles are congruent if ....

(a) All three corresponding angles are equal

(b) Two angles and a side of one are equal to two angles and a side of the other.

(d) One angle and two sides of one are equal to one angle and two sides of the other.

Answer: (c) Two angles and a side of one are equal to two angles and the corresponding side of the other.

[ Two angles and the corresponding side must be equal (ASA or AAS rule). ]

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