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प्रश्न
In the following figure, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

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उत्तर
Given, EG = FI
EG + GF = FI + GF ...[Adding GF on both sides]
EF = IG
In ΔDEF and ΔHIG,
DE = IH ...[Given]
EF = IG ...[Proved above]
∠E = ∠I ...[Given]
By SAS congruence criterion,
ΔDEF ≅ ΔHIG
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संबंधित प्रश्न
Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:
Construct a triangle XYZ with the given conditions.
BC = 8 cm, AC = 6 cm and ∠C = 40°
Construct a triangle PQR with given conditions.
∠Q = 90°, ∠R = 42° and QR = 5.5 cm
In ∆ABC and ∆PQR, ∠A = 50° = ∠P, PQ = AB, and PR = AC. By which property ∆ABC and ∆PQR are congruent?

In the following figure, AB = AD and ∠BAC = ∠DAC. Then
- ∆ ______ ≅ ∆ABC.
- BC = ______.
- ∠BCA = ______.
- Line segment AC bisects ______ and ______.
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- Is ∆PQR ≅ ∆PSR? Give reasons.
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