NCERT exercise 3.2 class 8 solution -students can click here to download the entire pdf chapterwise .here free pdf can be download for NCERT solution class 8. all Exercise are available here. These solutions are available in downloadable PDF format as well. it will help students in getting rid of all the doubts about those particular topics that are covered in the exercise. The NCERT textbook provides plenty of questions for the students to solve and practise. Solving and practising is more than enough to score high in the Class 8 examinations. Moreover, students should make sure that they practise every problem given in the textbook . exercise 3.2 class 8 solution Pdf can be downloaded free here.
Exercise 3.2 class 8 solution-exercise preview
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Exercise 3.2 class 8 solution- rhombus and its properties
A rhombus is a special type of parallelogram with four equal-length sides and opposite angles that are equal in measure. Here are the key properties of a rhombus:
- All sides are equal: In a rhombus, all four sides have the same length. This property distinguishes a rhombus from a general parallelogram.
- Opposite angles are equal: The opposite angles in a rhombus have equal measures. This means that if you have a pair of opposite angles, they are of the same size.
- Consecutive angles are supplementary: The consecutive (adjacent) angles in a rhombus add up to 180 degrees. In other words, they are supplementary angles.
- Diagonals bisect the angles: The diagonals of a rhombus bisect the interior angles. This means that when a diagonal intersects an angle, it divides that angle into two equal angles.
- Diagonals are perpendicular: The diagonals of a rhombus are perpendicular to each other, forming right angles at their point of intersection.
- Diagonals are of equal length: The diagonals of a rhombus are of equal length. This property distinguishes a rhombus from other types of quadrilaterals, such as a rectangle or a square.
- Opposite sides are parallel: Like all parallelograms, opposite sides of a rhombus are parallel to each other.
- The sum of the interior angles is 360 degrees: Just like in any quadrilateral, the sum of the four interior angles of a rhombus is equal to 360 degrees.
- The diagonals create four equal right-angled triangles: The diagonals of a rhombus divide it into four congruent right-angled triangles. Each of these triangles has a right angle (90 degrees) at the point of intersection of the diagonals.
These properties make the rhombus a special and versatile geometric shape, with characteristics that are often used in various mathematical and engineering applications.
Exercise 3.2 class 8 solution-solution pdf
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Exercise 3.2 class 8 solution -rectangle and its properties
A rectangle is a specific type of quadrilateral with four right angles and opposite sides that are equal in length. Here are the key properties of a rectangle:
- Four right angles: A rectangle has four right angles, which means each angle measures 90 degrees.
- Opposite sides are equal in length: In a rectangle, the pairs of opposite sides are of equal length. This property distinguishes a rectangle from a general parallelogram.
- Consecutive angles are supplementary: The consecutive (adjacent) angles in a rectangle add up to 180 degrees. This means that they are supplementary angles.
- Diagonals are equal in length: The diagonals of a rectangle are of equal length and bisect each other. This means that they divide each other into two equal segments, and each diagonal is twice as long as one side.
- Opposite sides are parallel: Just like in all parallelograms, the opposite sides of a rectangle are parallel to each other.
- The sum of the interior angles is 360 degrees: As with any quadrilateral, the sum of the four interior angles of a rectangle is equal to 360 degrees.
- All sides are of equal length: A rectangle is a special case of a parallelogram where all four sides have the same length.
- The diagonals are congruent: The diagonals of a rectangle are congruent, which means they have the same length.
- Each angle is a right angle: In a rectangle, all four angles are right angles (90 degrees).
- Opposite sides are equal in length and parallel: The combination of equal side lengths and parallel opposite sides makes rectangles especially useful in engineering and geometry.
- The area of a rectangle: The area of a rectangle can be calculated using the formula: Area = length × width, where “length” and “width” represent the two adjacent sides of the rectangle.
Rectangles are commonly encountered in everyday life and are widely used in various fields, including construction, engineering, and mathematics due to their well-defined properties and symmetry.