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Q2(i):
Give two different examples of pair of (i) similar figures.
Solution :
Given: The definition of similar figures in geometry, which states that two figures are similar if they have the same shape but not necessarily the same size.
To Find: Two distinct examples of pairs of similar figures.
Theoretical Context: Two polygons are said to be similar if:
1. Their corresponding angles are equal.
2. Their corresponding sides are in the same ratio (proportion).
Visual Representation:
Step 1: Identifying Example 1 - Equilateral Triangles
Let us consider two equilateral triangles, $\triangle PQR$ and $\triangle ABC$.
In any equilateral triangle, each interior angle is exactly $60^\circ$.
Since all angles in both triangles are $60^\circ$, the condition for equal corresponding angles is satisfied.
Furthermore, the ratio of corresponding sides $\frac{PQ}{AB} = \frac{QR}{BC} = \frac{RP}{CA}$ is constant.
Therefore, any two equilateral triangles are similar figures.
Step 2: Identifying Example 2 - Circles
Let us consider two circles with radii $r_1$ and $r_2$ respectively.
A circle is defined by the set of all points in a plane that are at a fixed distance (radius) from a fixed point (center).
Because all circles have the same round shape and lack corners, they are geometrically similar.
The ratio of their circumferences ($2\pi r_1 : 2\pi r_2$) and the ratio of their diameters ($2r_1 : 2r_2$) both simplify to the ratio of their radii ($r_1 : r_2$).
Therefore, any two circles are similar figures.
Final Answer: Two examples of pairs of similar figures are:
1. Any two equilateral triangles.
2. Any two circles.
More Questions from Class 10 Mathematics Triangles EXERCISE 6.1
- Q1(i): Fill in the blanks using the correct word given in brackets : (i) All circles are ______. (congruent, similar)
- Q1(ii): Fill in the blanks using the correct word given in brackets : (ii) All squares are ______. (similar, congruent)
- Q1(iii): Fill in the blanks using the correct word given in brackets : (iii) All ______ triangles are similar. (isosceles, equilateral)
- Q1(iv): Fill in the blanks using the correct word given in brackets : (iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are ______ and (b) their corresponding sides are ______. (equal, proportional)
- Q2(ii): Give two different examples of pair of (ii) non-similar figures.
- Q3: State whether the following quadrilaterals are similar or not:
CBSE Solutions for Class 10 Mathematics Triangles
Chapters in CBSE - Class 10 Mathematics
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