If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then
a. △PQR ~ △CAB
b. △PQR ~ △ABC
c. △CBA ~ △PQR
d. △BCA ~ △PQR
Solution:
Given, the two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ
We have to find the correct solution from the given options.
SSS criterion states that if three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar.
It is clear that the corresponding sides of the two triangles are equal.
By SSS criterion, the corresponding vertices are as follows:
A ↔ Q
B ↔ R
C ↔ P
Therefore, we have △PQR ~ △CAB
✦ Try This:Two triangles ABC and PQR are such that; AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Check whether the triangles are congruent.
Given, two triangles ABC and PQR
The length of the segments
AB = 3.5 cm
BC = 7.1 cm
AC = 5 cm
PQ = 7.1 cm
QR = 5 cm
PR = 3.5 cm
We have to check if the triangles are congruent.
From the given length of segments we observe that
AB = PR = 3.5 cm
BC = PQ = 7.1 cm
AC = QR = 5 cm
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, the two triangles ABC and PRQ are congruent
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 4
If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then, a. △PQR ~ △CAB, b. △PQR ~ △ABC, c. △CBA ~ △PQR, d. △BCA ~ △PQR
Summary:
If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then △PQR ~ △CAB.
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