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Exercise 3.1 class 8 solution-QUADRILATERAL
quadrilateral is a geometric shape with four sides and four vertices (corners). It is a two-dimensional polygon. Quadrilaterals can vary in shape and size, and there are various types of quadrilaterals, each with its own unique properties. Some common types of quadrilaterals include:
- Rectangle: A rectangle is a quadrilateral with four right angles. Opposite sides are of equal length.
- Square: A square is a special type of rectangle where all four sides are of equal length.
- Parallelogram: A parallelogram is a quadrilateral where opposite sides are parallel and of equal length.
- Rhombus: A rhombus is a parallelogram with all sides of equal length. Its opposite angles are also equal.
- Trapezoid: A trapezoid is a quadrilateral with one pair of parallel sides. The other two sides are not parallel.
- Kite: A kite is a quadrilateral with two pairs of adjacent sides that are of equal length.
- These are the most common types of quadrilaterals, but there are other more specialized types as well. The properties and characteristics of each type of quadrilateral can be used to solve various geometric problems and calculate different aspects of the shape, such as area, perimeter, and angles.
Exercise 3.1 class 8 solution-A parallelogram
A parallelogram is a type of quadrilateral with specific properties and characteristics. Here are the key properties of a parallelogram:
- Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that the pairs of sides facing each other never intersect.
- Opposite sides are equal in length: The lengths of the opposite sides of a parallelogram are equal. This property is a consequence of the sides being parallel.
- Opposite angles are equal: The angles formed between the opposite sides of a parallelogram are congruent, which means they have the same measure. In other words, if you have a pair of opposite angles, they are of equal size.
- Consecutive angles are supplementary: The consecutive (adjacent) angles in a parallelogram add up to 180 degrees. This property is also known as the opposite angles being supplementary.
- Diagonals bisect each other-he diagonals of a parallelogram (lines connecting opposite vertices) intersect at their midpoint. This means they divide each other into two equal segments.
- Opposite sides are of equal length: In a parallelogram, not only are the opposite sides parallel, but they are also of equal length. This is sometimes referred to as the “opposite sides are congruent.”
- The sum of the interior angles is 360 degrees: The four interior angles of a parallelogram add up to 360 degrees. This is because the opposite angles are congruent, and the consecutive angles are supplementary.
- The diagonals create equal triangles: The two triangles formed by the diagonals of a parallelogram are equal in area and shape.
- The opposite sides have equal slopes: If you were to graph a parallelogram on a coordinate plane, the slopes of the opposite sides would be equal.
These properties make the parallelogram a versatile shape with several geometric characteristics that can be useful in various mathematical and engineering applications.