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Q1(ii):
Fill in the blanks using the correct word given in brackets : (ii) All squares are ______. (similar, congruent)
Solution :
Given: A set of geometric figures known as squares.
To Find: The correct term to describe the relationship between all squares, choosing between "similar" and "congruent".
Step 1: Defining Similarity of Polygons
Two polygons are said to be similar if:
1. Their corresponding angles are equal.
2. Their corresponding sides are in the same ratio (proportion).
[Definition of Similar Polygons]
Step 2: Analyzing the Properties of Squares
Let $S_1$ and $S_2$ be two squares with side lengths $a_1$ and $a_2$ respectively.
- All interior angles of any square are $90^\circ$. Therefore, the corresponding angles of $S_1$ and $S_2$ are equal ($90^\circ = 90^\circ$).
- The ratio of corresponding sides is $\frac{a_1}{a_2}$. Since all sides of a square are equal, the ratio of all pairs of corresponding sides is constant, i.e., $\frac{a_1}{a_2} = \frac{a_1}{a_2} = \frac{a_1}{a_2} = \frac{a_1}{a_2}$.
[Since all squares satisfy the criteria for similarity]
Step 3: Evaluating Congruence
Two figures are congruent if they have the same shape and the same size. Since squares can have different side lengths (e.g., a square of side 2cm and a square of side 5cm), they are not necessarily congruent.
[Definition of Congruent Figures]
Step 4: Conclusion
Because all squares possess the same shape (equiangular and proportional sides) but not necessarily the same size, they are classified as similar figures.
[Logical deduction based on geometric definitions]
Final Answer: All squares are similar.
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(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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