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प्रश्न
ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent
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उत्तर
In ΔABC ∠B = 60° and ∠C = 70°
∴ ∠A = 180° – (60° + 70°)
= 180° – 130°
= 50°
In ΔDEF ∠E = 70° and ∠D = 60°
∠F = 180° – (70° + 60°)
= 180° – 130°
= 50°
∠A = ∠F = 50°
∠B = ∠D = 60°
∠C = ∠E = 70°
By AAA congruency
ΔABC ≅ ΔFDE
or
∠B = ∠D = 60°
∠C = ∠E = 70°
AB = FE
By ASA congruency
ΔABC ≅ ΔFDE
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संबंधित प्रश्न
In Fig, can you use the ASA congruence rule and conclude that ∆AOC ≅ ∆BOD?
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by the ASA congruence rule. In the case of congruence, write it in symbolic form.
∆DEF, ∠D = 60º, ∠F = 80º, DF = 6 cm.
∆PQR, ∠Q = 60º, ∠R = 80º, QP = 6 cm.
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:
For the given pair of triangles state the criterion that can be used to determine the congruency?
If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
AAS congruence criterion is same as ASA congruence criterion.
In the following figure, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
In the following figure, ∠1 = ∠2 and ∠3 = ∠4.
- Is ∆ADC ≅ ∆ABC? Why ?
- Show that AD = AB and CD = CB.
