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Key Points About Quadrilaterals
1. Sum of the angles of a quadrilateral is 360°.
2. A diagonal of a parallelogram divides it into two congruent triangles.
3. In a parallelogram,
(i) opposite sides are equal
(ii) opposite angles are equal
(iii) diagonals bisect each other
4. A quadrilateral is a parallelogram, if
(i) opposite sides are equal or
(ii) opposite angles are equal or
(iii) diagonals bisect each other or
(iv) a pair of opposite sides is equal and parallel
5. Diagonals of a rectangle bisect each other and are equal and vice-versa.
6. Diagonals of a rhombus bisect each other at right angles and vice-versa.
7. Diagonals of a square bisect each other at right angles and are equal, and vice-versa.
8. The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.
9. A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
10. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a parallelogram.
FAQs on Key Points About Quadrilaterals, Class 9, Maths
| 1. What are the key points to remember about quadrilaterals in class 9 mathematics? |  |
Ans. The key points to remember about quadrilaterals in class 9 mathematics are:
- A quadrilateral is a polygon with four sides and four vertices.
- The sum of the interior angles of a quadrilateral is always 360 degrees.
- There are different types of quadrilaterals such as parallelograms, rectangles, squares, rhombuses, and trapezoids.
- In a parallelogram, opposite sides are parallel and opposite angles are equal.
- In a rectangle, all angles are right angles.
- In a square, all sides are equal and all angles are right angles.
- In a rhombus, all sides are equal but the angles are not necessarily right angles.
- In a trapezoid, only one pair of opposite sides are parallel.
| 2. What is the sum of the interior angles of a quadrilateral? | |
Ans. The sum of the interior angles of a quadrilateral is always 360 degrees. This means that if we measure the angles of a quadrilateral and add them together, the total will always be 360 degrees.
| 3. What are the different types of quadrilaterals? | |
Ans. There are different types of quadrilaterals, including:
- Parallelogram: In a parallelogram, opposite sides are parallel and opposite angles are equal.
- Rectangle: In a rectangle, all angles are right angles.
- Square: In a square, all sides are equal and all angles are right angles.
- Rhombus: In a rhombus, all sides are equal but the angles are not necessarily right angles.
- Trapezoid: In a trapezoid, only one pair of opposite sides are parallel.
| 4. How do we determine if a quadrilateral is a parallelogram? | |
Ans. To determine if a quadrilateral is a parallelogram, we need to check if its opposite sides are parallel and if its opposite angles are equal. If both of these conditions are satisfied, then the quadrilateral is a parallelogram.
| 5. What are the properties of a square? | |
Ans. The properties of a square include:
- All sides of a square are equal in length.
- All angles of a square are right angles.
- The diagonals of a square are equal in length and bisect each other at right angles.
- The diagonals of a square divide it into four congruent right-angled triangles.
- The perimeter of a square is four times the length of its side.
- The area of a square is the square of its side length.
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