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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)
Solution :
Given: Two polygons having the same number of sides ($n$).
To Find: The conditions under which these two polygons are considered similar.
Step 1: Understanding the Definition of Similar Polygons
In geometry, two polygons with the same number of sides are defined as similar if and only if they satisfy two specific criteria simultaneously. Similarity implies that the shapes are identical in form but not necessarily in size (i.e., one is a scaled version of the other).
Step 2: Analyzing Condition (a) - Corresponding Angles
For two polygons to be similar, their internal structure must maintain the same "shape." This is preserved if the angles at each corresponding vertex are identical. If the angles were different, the polygons would be distorted relative to each other. Therefore, the corresponding angles must be equal.
Step 3: Analyzing Condition (b) - Corresponding Sides
While the angles define the shape, the sides define the scale. For the polygons to be similar, the ratio of the lengths of any two corresponding sides must be constant. This constant ratio is known as the scale factor. Therefore, the corresponding sides must be proportional.
Step 4: Synthesizing the Statement
Based on the geometric definition of similarity for polygons:
(a) Their corresponding angles are equal.
(b) Their corresponding sides are proportional.
Final Answer: Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional.
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)
- 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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