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Q1(i):
Fill in the blanks using the correct word given in brackets : (i) All circles are ______. (congruent, similar)
Solution :
Given: A set of geometric figures defined as circles of varying radii.
To Find: Determine whether all circles are "congruent" or "similar" by filling in the blank.
Step 1: Defining Congruency
Two geometric figures are said to be congruent if they have the same shape and the same size. For two circles to be congruent, their radii must be equal ($r_1 = r_2$).
Step 2: Defining Similarity
Two geometric figures are said to be similar if they have the same shape, but not necessarily the same size. In the case of circles, every 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 possess the same round shape, they satisfy the condition of similarity regardless of their radius.
Step 3: Logical Deduction
Since circles can have different radii (as shown in the diagram where $r_1=30$ and $r_2=50$), they cannot be congruent in all cases. However, because the ratio of the corresponding parts (the circumference to the diameter, which is $\pi$) remains constant for all circles, they are always similar.
Step 4: Conclusion
Based on the definition of similarity in geometry, all circles are similar because they share the same shape, even if their sizes differ.
Final Answer: All circles are similar.
More Questions from Class 10 Mathematics Triangles EXERCISE 6.1
- 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.
- 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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