Match the following based on the construction of similar triangles, if scale factor $(\frac{m}{n})$ is
$\begin{matrix} I . > 1 & a) T h e s i m i l a r t r i a n g l e i s s m a l l e r t h a n t h e o r i g i n a l t r i a n g l e . I I . < 1 & b) T h e t w o t r i a n g l e s a r e c o n g r u e n t t r i a n g l e s . I I I . = 1 & c) T h e s i m i l a r t r i a n g l e i s l a r g e r t h a n t h e o r i g i n a l t r i a n g l e . \end{matrix}$

$I - a, I I - c, I I I - b$

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$I - b, I I - a, I I I - c$

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$I - c, I I - a, I I I - b$

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$I - a, I I - b, I I I - c$

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Solution

The correct option is C
$I - c, I I - a, I I I - b$

Scale factor basically defines the ratio between the sides of the constructed triangle to that of the original triangle.

So when we see the scale factor $(\frac{m}{n}) > 1$ , it means the sides of the constructed triangle is larger than the original triangle i.e., the triangle constructed is larger than the original triangle.

Similarly, if scale factor $(\frac{m}{n}) < 1$ , then the sides of the constructed triangle is smaller than that of the original triangle i.e., the constructed triangle is smaller than the original triangle.

When we have scale factor $(\frac{m}{n}) = 1$ , then the sides of both the constructed triangle and that of the original triangle is equal.

When a pair of similar triangles have equal corresponding sides, then the pair of similar triangles can be called as congruent because then the triangles will have equal corresponding sides and equal corresponding angles.

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Similar questions

Match the following based on the construction of similar triangles, if scale factor ( $\frac{m}{n}$ ) is

I. >1

II. <1

III. =1

a) The similar triangle is smaller than the original triangle.

b) The two triangles are congruent triangles.

c) The similar triangle is larger than the original triangle.

Match the following based on the construction of similar triangles, if scale factor $(\frac{m}{n})$ is
$\begin{matrix} I . > 1 & a) T h e s i m i l a r t r i a n g l e i s s m a l l e r t h a n t h e o r i g i n a l t r i a n g l e . I I . < 1 & b) T h e t w o t r i a n g l e s a r e c o n g r u e n t t r i a n g l e s . I I I . = 1 & c) T h e s i m i l a r t r i a n g l e i s l a r g e r t h a n t h e o r i g i n a l t r i a n g l e . \end{matrix}$

Q. If a triangle PQR is constructed similar to triangle ABC and is smaller than the triangle ABC, then the scale factor is .

Q. In construction of similar triangles, if scale factor is more than 1, then the new triangle is the given one.

Match the following based on the construction of similar triangles, if scale factor is $(\frac{m}{n})$ .

$\begin{matrix} I . \frac{m}{n} > 1 & a) T h e s i m i l a r t r i a n g l e i s s m a l l e r t h a n t h e o r i g i n a l t r i a n g l e . I I . \frac{m}{n} < 1 & b) T h e t w o t r i a n g l e s a r e c o n g r u e n t t r i a n g l e s . I I I . \frac{m}{n} = 1 & c) T h e s i m i l a r t r i a n g l e i s l a r g e r t h a n t h e o r i g i n a l t r i a n g l e . \end{matrix}$

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Match the following based on the construction of similar triangles, if scale factor (mn) is I. >1a) The similar triangle is smaller than the original triangle.II. <1b) The two triangles are congruent triangles.III. =1c) The similar triangle is larger than the original triangle.