If in triangles ABC and DEF, AB/DE = BC/FD, then they will be similar, when
a. ∠B = ∠E
b. ∠A = ∠D
c. ∠B = ∠D
d. ∠A = ∠F
Solution:
Given, the triangles ABC and DEF
Also, AB/DE = BC/FD
We have to choose the correct condition so the triangles will be similar.
SSS criterion states that if three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar.
By SSS criterion,
AB/DE = BC/DF = AC/EF
We know that similar triangles have congruent corresponding angles and the corresponding sides are in proportion.
So, ∠A = ∠E
∠B = ∠D
∠C = ∠F
So, option C is true.
Therefore, the triangles to be similar when ∠B = ∠D.
✦ Try This: If in triangles ABC and PQR, AB/PQ = BC/PR , then they will be similar, when
a. ∠B = ∠R
b. ∠C = ∠P
c. ∠B = ∠P
d. ∠A = ∠Q
Given, the triangles ABC and PQR
Also, AB/PQ = BC/PR
We have to choose the correct condition so the triangles will be similar.
SSS criterion states that if three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar.
By SSS criterion,
AB/PQ = BC/PR = AC/QR
We know that similar triangles have congruent corresponding angles and the corresponding sides are in proportion.
So, ∠A = ∠Q
∠B = ∠P
∠C = ∠R
Therefore, the triangles are similar when ∠B = ∠P
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 10
If in triangles ABC and DEF, AB/DE = BC/FD , then they will be similar, when, a. ∠B = ∠E, b. ∠A = ∠D, c. ∠B = ∠D, d. ∠A = ∠F
Summary:
If in triangles ABC and DEF, AB/DE = BC/FD , then they will be similar, when ∠B = ∠D
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