Similar Triangles and Corresponding Sides

Similar triangles are those triangles that have the same shape but may have different sizes. When two triangles are similar, the corresponding angles are the same, and the corresponding sides are proportional. In other words, the ratio of the lengths of the corresponding sides is the same for all pairs of corresponding sides. This ratio is called the scale factor.

Given the statement that "Two congruent triangles are actually similar triangles with the ratio of corresponding sides as," we are asked to determine the scale factor for the corresponding sides of the two triangles.

Option B is the correct answer, and the scale factor is 1:1. This means that the corresponding sides of the two triangles are equal in length.

Explanation of Other Options:

a) 1:2 - This means that the corresponding sides of one triangle are twice as long as the corresponding sides of the other triangle. Therefore, the triangles are not congruent, but they are similar.

c) 1:3 - This means that the corresponding sides of one triangle are three times as long as the corresponding sides of the other triangle. Therefore, the triangles are not congruent, but they are similar.

d) 2:1 - This means that the corresponding sides of one triangle are half as long as the corresponding sides of the other triangle. Therefore, the triangles are not congruent, but they are similar.

Conclusion:

In summary, when two triangles are congruent, they are also similar with a scale factor of 1:1. This means that the corresponding sides of the triangles are equal in length.

Let us take two triangles
ABC and PQR
if they are congruent
therefore,
AB=PQ (BY CPCT) --------------eqn 1
BC=QR(-----do-----)----------------eqn 2
AC=PR(-----do-----)----------------eqn 3

let us divide area of both triangles
at(ABC)/ar(PQR) = 1:1 (AREA OF CONGRUENT TRIANGLES ARE EQUAL)

divide AB by PQ
AB/PQ=AB/AB=1/1 (From eqn 1)
Similarly,
BC/QR=1/1
AC/PR =1/1

HP