In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. 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
Solution:
Given, in the triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C
Also, AB = 3DE
We have to find if the triangles are similar and congruent or not.
AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.
By AAA criterion,
As ∠B = ∠E and ∠F = ∠C, the third angle will also be equal.
i.e.∠D = ∠A
Therefore, the triangles ABC and DEF are similar.
It is given that AB = 3DE
It is clear that the sides AB and DE are not equal
So, the triangles are not congruent.
Therefore, the triangles ABC and DEF are similar but not congruent.
✦ Try This: In triangles ABC and PQR, ∠B = ∠Q, ∠C = ∠R and AB = 3 PQ. 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
Given, in the triangles ABC and DEF, ∠B = ∠Q, ∠C = ∠R
Also, AB = 3PQ
We have to find if the triangles are similar and congruent or not.
AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.
By AAA criterion,
As ∠B = ∠Q and ∠C = ∠R, the third angle will also be equal.
i.e.∠P = ∠A
Therefore, the triangles ABC and PQR are similar.
It is given that AB = 3PQ
It is clear that the sides AB and PQ are not equal
So, the triangles are not congruent.
Therefore, the triangles ABC and PQR are similar but not congruent
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 7
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. 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
Summary:
In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. Then, the two triangles are Similar but not congruent.
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