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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
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using the SAS congruence rule. If the triangles are congruent, write them in symbolic form.
∆ABC, AB = 7 cm, BC = 5 cm, ∠B = 50°.
∆DEF, DE = 5 cm, EF = 7 cm, ∠E = 50°.
In Fig,
AB = AC and AD is the bisector of ∠BAC.
(i) State three pairs of equal parts in triangles ADB and ADC.
(ii) Is ∆ADB ≅ ∆ADC? Give reasons.
(iii) Is ∠B = ∠C? Give reasons.
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:
In the given figure, ΔBCD is isosceles with base BD and ∠BAE ≡∠DEA. Prove that AB ≡ ED
Construct a triangle PQR with given conditions.
∠P = 115°, ∠Q = 40° and PQ = 6 cm
Construct a triangle PQR with given conditions.
∠Q = 90°, ∠R = 42° and QR = 5.5 cm
In the following figure, ΔPQR ≅ Δ ______.
In the following figure, which pairs of triangles are congruent by SAS congruence criterion (condition)? if congruent, write the congruence of the two triangles in symbolic form.
State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).
∆ABC: AB = 4.8 cm, ∠A = 90°, AC = 6.8 cm
∆XYZ: YZ = 6.8 cm, ∠X = 90°, ZX = 4.8 cm
In the following figure, PQ = PS and ∠1 = ∠2.
- Is ∆PQR ≅ ∆PSR? Give reasons.
- Is QR = SR? Give reasons.
