Match the following based on the construction of similar triangles- if scale factor is m - n - begin array -c- - hlineII- - frac m n - 1 - b - The two triangles are congruent triangles- Nllhlineend array A- I- a- II - b- III - cB- I- c- II - a- III - bC- I- a- II - c- III - bD- I- b- II - a- III - C

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Construction of a Similar Triangle, When One Vertex Is Common

Match the fol...

Question

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

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

I- c, II - a, III - b

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I- b, II - a, III - c

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I- a, II - c, III - b

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I- a, II - b, III - c

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Solution

The correct option is A
I- c, II - a, III - 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 is greater than 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 m/n is smaller than 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.

And when we have scale factor equal to 1, then the sides of both the constructed triangle and that of the original triangle is equal.
When a pair of similar triangles have their equal corresponding sides, then the pair of similar triangles can be called as congruent because the triangles 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
$\begin{matrix} I . > 1 & a) T h e s i m i l a r t r i a n g l e i s s m a l l e r t h a n t h e o r i g i n a l t r i a n g l e . I I . < 1 & b) T h e t w o t r i a n g l e s a r e c o n g r u e n t t r i a n g l e s . I I I . = 1 & c) T h e s i m i l a r t r i a n g l e i s l a r g e r t h a n t h e o r i g i n a l t r i a n g l e . \end{matrix}$

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.

Q. In the construction of triangle similar and larger to a given triangle as per given scale factor m : n, the construction is possible only when :

Question 3
Draw a $Δ$ ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$ .
Thinking process
Here, scale factor = $\frac{m}{n} = \frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

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