Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > Important Formulas: Lines and Angles
Important Formulas: Lines and Angles | Mathematics (Maths) Class 7 PDF Download
Important Formulas
(1) A line which intersects two or more given lines at distinct points is called a transversal to the given lines.
(2) Lines in a plane are parallel if they do not intersect when produced indefinitely in either direction.
(3) The distance between two intersecting lines is zero.
(4) The distance between two parallel lines is the same everywhere and is equal to the perpendicular distance between them.
(5) If two parallel lines are intersected by a transversal then
- pairs of alternate (interior or exterior) angles are equal.
- pairs of corresponding angles are equal.
- interior angles on the same side of the transversal are supplementary.
(6) If two non-parallel lines are intersected by transversal then none of (i), (ii) and (iii) hold true in 5.
(7) If two lines are intersected by a transversal, then they are parallel if any one of the following is true:
- The angles of a pair of corresponding angles are equal.
- The angles of a pair of alternate interior angles are equal.
- The angles of a pair of interior angles on the same side of the transversal are supplementary.
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FAQs on Important Formulas: Lines and Angles - Mathematics (Maths) Class 7
| 1. What are some important formulas for lines and angles? |  |
Ans. Some important formulas for lines and angles include:
- Angle sum property of a triangle: The sum of the angles in a triangle is always 180 degrees.
- Exterior angle property of a triangle: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
- Vertical angles property: Vertical angles are always congruent, which means they have the same measure.
- Linear pair property: If two angles form a linear pair, the sum of their measures is always 180 degrees.
- Corresponding angles property: If two lines are cut by a transversal, then the pairs of corresponding angles are congruent.
| 2. How can the angle sum property of a triangle be used to find unknown angles? | |
Ans. The angle sum property of a triangle states that the sum of the angles in a triangle is always 180 degrees. To find unknown angles using this property, you can follow these steps:
1. Identify the known angles in the triangle.
2. Add the measures of the known angles.
3. Subtract the sum obtained in step 2 from 180 degrees.
4. The result will be the measure of the unknown angle.
| 3. What is the exterior angle property of a triangle? | |
Ans. The exterior angle property of a triangle states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it. In other words, if you extend one side of a triangle, the angle formed by the extension and the adjacent side is equal to the sum of the two opposite interior angles.
| 4. How can the corresponding angles property be used to solve problems involving parallel lines and transversals? | |
Ans. The corresponding angles property states that if two lines are cut by a transversal, then the pairs of corresponding angles are congruent. This property can be used to solve problems involving parallel lines and transversals by following these steps:
1. Identify the pairs of corresponding angles in the given figure.
2. Set up an equation by equating the measures of the corresponding angles.
3. Solve the equation to find the value of the unknown angle.
| 5. What is the linear pair property and how can it be applied to find unknown angles? | |
Ans. The linear pair property states that if two angles form a linear pair (adjacent angles with a common side), the sum of their measures is always 180 degrees. To find unknown angles using this property, you can follow these steps:
1. Identify the linear pair of angles in the given figure.
2. Set up an equation by equating the sum of their measures to 180 degrees.
3. Solve the equation to find the value of the unknown angle.
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