GSEB Class 10 Maths Solutions Chapter 6 Triangle Exercise 6.1

Question 1. Fill in the blanks using the correct word given in brackets.
1. All circles are __________ (congruent, similar)
2. All squares are __________ (similar, congruent)
3. All __________ triangles are similar (isosceles, equilateral)
4. Two polygons of the same number of sides are similar. If (a) their corresponding angles are __________ and (b) their corresponding sides are __________ (equal, proportional)
Answer:
1. Similar
2. Similar
3. Equilateral
4. (a) equal (b) proportional.
In simple words: This question tests your knowledge of similar shapes. Circles and squares are always similar to each other, no matter their size. Equilateral triangles, which have all sides and angles the same, are also always similar to each other. For two polygons to be similar, their matching angles must be equal, and their matching sides must be in the same proportion.

Exam Tip: Remember the two key conditions for similarity in polygons: corresponding angles must be equal, and corresponding sides must be proportional. Apply these rules carefully for each blank.

Question 2. Give two different examples of pair of
(i) Similar figure
(ii) Non-similar figure.
Answer:
(i) Examples of similar figures:
(a) Two equilateral triangles are similar.
(b) Two squares are similar.
(ii) Examples of non-similar figures:
(a) Two triangles, for example, one scalene and another isosceles triangle.
(b) Two rectangles, like one square and another non-square rectangle.
In simple words: Similar figures have the same shape but can be different sizes. Non-similar figures have different shapes. For similar figures, think about shapes where all versions are geometrically the same, like squares or equilateral triangles. For non-similar ones, consider shapes where varying their proportions changes their fundamental appearance, like a very thin rectangle versus a square, or triangles with completely different side lengths and angles.

Exam Tip: When giving examples, choose common geometric shapes. For similar figures, pick those with fixed angle properties (e.g., all squares, all circles). For non-similar figures, select shapes that can have varying angles or proportions, like a rhombus and a square, or an isosceles and a scalene triangle.

Question 3. State whether the following quadrilaterals are similar or not.
Answer: The given quadrilaterals are not similar. The first figure is a rhombus (all sides 1.5 cm), and the second figure is a square (all sides 3 cm). Although their sides are proportional (1:2 ratio), their corresponding angles are not equal. For instance, the angles of a rhombus are generally not 90 degrees, while all angles in a square are 90 degrees. Therefore, since the angles differ, the figures are not similar.
In simple words: The two shapes are not similar. Even though their side lengths are in a steady ratio (the bigger one's sides are twice the smaller one's), their angles are not the same. The first shape is a rhombus, and the second is a square. Because their corner angles don't match, they cannot be called similar.

Exam Tip: To determine if two polygons are similar, always check both conditions: (1) corresponding angles must be equal, and (2) corresponding sides must be proportional. If even one condition is not met, the figures are not similar. In this case, the angles were the differentiating factor.