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Q2(ii):
Give two different examples of pair of (ii) non-similar figures.
Solution :
Given: The requirement to provide two distinct examples of pairs of non-similar figures.
To Find: Two pairs of geometric figures that do not satisfy the criteria for similarity.
Theoretical Context: Two polygons are said to be similar if:
- Their corresponding angles are equal.
- Their corresponding sides are in the same ratio (i.e., proportional).
If either of these conditions is violated, the figures are classified as non-similar.
Step 1: Analyzing Example 1 (Scalene Triangle and Equilateral Triangle)
Let $T_1$ be a scalene triangle with side lengths $3\text{ cm}, 4\text{ cm},$ and $5\text{ cm}$.
Let $T_2$ be an equilateral triangle with side lengths $4\text{ cm}, 4\text{ cm},$ and $4\text{ cm}$.
Justification:
- The corresponding angles of $T_1$ are not equal to the corresponding angles of $T_2$. In $T_2$, all angles are $60^\circ$, whereas in $T_1$, the angles are approximately $36.87^\circ, 53.13^\circ,$ and $90^\circ$.
- The ratio of corresponding sides is not constant: $\frac{3}{4} \neq \frac{4}{4} \neq \frac{5}{4}$.
Since neither condition for similarity is met, these figures are non-similar.
Step 2: Analyzing Example 2 (Rectangle and Rhombus)
Let $R_1$ be a rectangle with sides $4\text{ cm}$ and $2\text{ cm}$.
Let $R_2$ be a rhombus with all sides equal to $3\text{ cm}$.
Justification:
- In a rectangle, all interior angles are $90^\circ$. In a rhombus (that is not a square), the interior angles are not $90^\circ$.
- Because the corresponding angles are not equal, the figures cannot be similar, regardless of the side ratios.
Summary of Findings:
| Pair | Figure A | Figure B | Reason for Non-Similarity |
|---|---|---|---|
| 1 | Scalene Triangle | Equilateral Triangle | Angles are unequal; sides are not proportional. |
| 2 | Rectangle | Rhombus | Corresponding angles are not equal. |
Final Answer: Two examples of pairs of non-similar figures are (1) a scalene triangle and an equilateral triangle, and (2) a rectangle and a rhombus.
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(i): Give two different examples of pair of (i) 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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