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प्रश्न
Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE
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उत्तर
In ∆ABC and ∆EBD,
AB = EB
BC = BD
∠ABC = ∠EBD ...[∵ Vertically opposite angles]
By SAS congruency criteria ∆ABC ≅ ∆EBD.
We know that corresponding parts of congruent triangles are congruent.
∴ ∠BCA ≅ ∠BDE and ∠BAC ≅ ∠BED
∠BCA ≅ ∠BDE means that alternate interior angles are equal if CD is the transversal to lines AC and DE.
Similarly, if AE is the transversal to AC and DE,
we have ∠BAC ≅ ∠BED
Again interior opposite angles are equal.
We can conclude that AC is parallel to DE.
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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 = 4.5 cm, AC = 4 cm, ∠A = 60°.
∆DEF, DE = 4 cm, FD = 4.5 cm, ∠D = 55°.
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
For the given pair of triangles state the criterion that can be used to determine the congruency?
Construct a triangle PQR with given conditions.
∠P = 60°, ∠R = 35° and PR = 7.8 cm
In the following figure, ΔPQR ≅ Δ ______.
State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).
∆PQR: PQ = 3.5 cm, QR = 4.0 cm, ∠Q = 60°
∆STU: ST = 3.5 cm, TU = 4 cm, ∠T = 60°
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, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?
