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Linear Equations in Two Variables
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Quadrilaterals
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Another Condition for a Quadrilateral to Be a Parallelogram
- The Mid-point Theorem
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Area
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- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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Statistics and Probability
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definition
- Linear Equation in One Variable: If there is only one variable in the equation then it is called a linear equation in one variable.
notes
Linear Equation in One Variable:
If there is only one variable in the equation then it is called a linear equation in one variable. These are called linear equations in one variable because the highest degree of the variable is one.
These are linear expressions:
2x, 2x + 1, 3y – 7, 12 – 5z, `5/4(x - 4) + 10`
These are not linear expressions:
x2 + 1, y + y2, 1 + z + z2 + z3. ....(since highest power of variable > 1)
The general form is ax + b = c, where a, b and c are real numbers and a ≠ 0.
Example:
x + 5 = 10, y – 3 = 19.
Some Important points related to Linear Equations:
-
There is an equality sign in the linear equation. The expression on the left of the equal sign is called the LHS (left-hand side) and the expression on the right of the equal sign is called the RHS (right-hand side).
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In the linear equation, the LHS is equal to RHS but this happens for some values only and these values are the solution of these linear equations.
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