Understand Parallel Lines, Transversal and Axioms. Click on the Link to Watch the VIDEO explanation:
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Concept Of Parallel Lines, Transversal and Axioms
Let us now learn some Concept Of Parallel Lines and Transversal and also some Axioms on parallel lines
Two lines are parallel to each other if, they lie on the same plane i.e., they are co-planer.
They do not meet, however far they are produced on either side.
Here AB and CD are parallel lines.
A transversal is a line that intersects two or more lines at distinct points. In the given figure, XY is a transversal.
The four pairs of angles 1 and 5, 2 and 6, 4 and 7, 3and 8 are called corresponding angles. The corresponding angles are similarly situated.
The two pairs of angles 2 and 8, 4 and 5 are called alternate angles. The alternate angles occur in Z formation.
The two pairs 2 and 5, 4 and 8 are called pairs of interior angles on the same side of the transversal.
Corresponding Angles Axiom
If two parallel lines cut by a transversal, then the corresponding angles are equal.
Hence, in the given figure angle 1 is equal to angle 5, angle 4 is equal to angle8, angle 2 is equal to angle6 and angle 3 is equal to angle 7.
Converse of the above Axiom
A transversal intersects two lines and if the corresponding angles are equal, then the lines are parallel.
If any one pair of corresponding angles are equal, then AB is parallel to CD.
Alternate Angles Axiom
If two parallel lines cut by a transversal, the alternate angles are equal.
Observe the figure AB is parallel to CD.
Angle 1 and Angle 3
Angle 2 and Angle 4
Are the two pairs of the alternate angles.
Angle 1 is equal to Angle 3 and
Angle 2 is equal to Angle 4.
Converse of the above Axiom
A transversal intersects two lines. If the alternate angles are equal, then the lines are parallel.
If angle1 is equal to angle 3 and angle 2 is equal to angle 4. AB is parallel to CD.
Allied Angles Axiom
Interior angles on the same side of a transversal are called allied angles.
The Allied Angles Axiom that if two parallel lines cuts by a transversal, then the allied angles are supplementary.
Observe the figure
Angle 1 plus Angle 2 is equal to 180 degree and
Angle 3 plus Angle 4 is equal to 180 degree.
Converse of the above Axiom
A transversal cuts two lines. If the allied angles are supplementary, then the lines are parallel. Again Observe the given figure if
Angle 1 plus Angle 2 is equal to 180 degree
Angle 3 plus Angle 4 is equal to 180 degree. Then AB is parallel to CD.
Watch Video
Concept Of Parallel Lines, Transversal and Axioms
Let us now learn some Concept Of Parallel Lines and Transversal and also some Axioms on parallel lines
Two lines are parallel to each other if, they lie on the same plane i.e., they are co-planer.
They do not meet, however far they are produced on either side.
Here AB and CD are parallel lines.
A transversal is a line that intersects two or more lines at distinct points. In the given figure, XY is a transversal.
The four pairs of angles 1 and 5, 2 and 6, 4 and 7, 3and 8 are called corresponding angles. The corresponding angles are similarly situated.
The two pairs of angles 2 and 8, 4 and 5 are called alternate angles. The alternate angles occur in Z formation.
The two pairs 2 and 5, 4 and 8 are called pairs of interior angles on the same side of the transversal.
Corresponding Angles Axiom
If two parallel lines cut by a transversal, then the corresponding angles are equal.
Hence, in the given figure angle 1 is equal to angle 5, angle 4 is equal to angle8, angle 2 is equal to angle6 and angle 3 is equal to angle 7.
Converse of the above Axiom
A transversal intersects two lines and if the corresponding angles are equal, then the lines are parallel.
If any one pair of corresponding angles are equal, then AB is parallel to CD.
Alternate Angles Axiom
If two parallel lines cut by a transversal, the alternate angles are equal.
Observe the figure AB is parallel to CD.
Angle 1 and Angle 3
Angle 2 and Angle 4
Are the two pairs of the alternate angles.
Angle 1 is equal to Angle 3 and
Angle 2 is equal to Angle 4.
Converse of the above Axiom
A transversal intersects two lines. If the alternate angles are equal, then the lines are parallel.
If angle1 is equal to angle 3 and angle 2 is equal to angle 4. AB is parallel to CD.
Allied Angles Axiom
Interior angles on the same side of a transversal are called allied angles.
The Allied Angles Axiom that if two parallel lines cuts by a transversal, then the allied angles are supplementary.
Observe the figure
Angle 1 plus Angle 2 is equal to 180 degree and
Angle 3 plus Angle 4 is equal to 180 degree.
Converse of the above Axiom
A transversal cuts two lines. If the allied angles are supplementary, then the lines are parallel. Again Observe the given figure if
Angle 1 plus Angle 2 is equal to 180 degree
Angle 3 plus Angle 4 is equal to 180 degree. Then AB is parallel to CD.
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