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In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are
- a)congruent but not similar
- b)similar but not congruent
- c)neither congruent nor similar
- d)congruent as well as similar
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3D...
to be congruent, the conditions are
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Hypotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, given triangles are not congruent.
But they are similar.
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Hypotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, given triangles are not congruent.
But they are similar.
Most Upvoted Answer
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3D...
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Community Answer
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3D...
Angle B = Angle E & Angle C = Angle F.
Therefore, by angle sum property, Angle A = Angle D
Therefore, the 2 triangles are similar.
But AB = 3DE
That means that sides are not equal.
But in congruent triangles, angles and sides must be equal
Hence, the triangles are similar but not congruent.
Hope you get this answer useful.
Thank you.
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In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles area)congruent but not similarb)similar but not congruentc)neither congruent nor similard)congruent as well as similarCorrect answer is option 'B'. Can you explain this answer?
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