In the picture transversal AD intersects two parallel PQ and RS at points B and C respectively.
According the given axiom
Angle ABQ (angle 1) = Angle BCS (angle 2) because they are corresponding angles
Angle QBC (angle 3) = Angle SCD (angle 4) because they are corresponding angles
There are two more pairs of corresponding angles. Can you find them?
Angle ABP = Angle BCR
Angle PBC = Angle RCD
Converse of the axiom: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
Given that XY is a transversal and it intersecting two lines PQ and RS at M and N respectively such that
Angle XMQ ( angle 1) = Angle MNS (angle 2)
PQ II RS ( PQ is parallel to RS)
Theorem 1 : If a transversal intersects two parallel lines then each pair of alternate interior angles is equal.
In the above picture AB and CD are two parallel lines. Transversal PS is intersecting AB and CD at points Q and R respectively.
Then according the theorem:
Angle CRQ = Angle RQB (Alternate interior angles)
There is one more pair of alternate interior angles. Can you find?
YES! Angle AQR = Angle QRD
Theorem 2 : If a transversal intersects two parallel lines ,then the each pair the interior angles on the same side of the transversal is supplementary ( In other words their sum is 180 degree)
In the above picture MN and XY are two parallel lines.Transversal PS is intersecting MN and XY at points Q and R respectively.Then according the theorem:
Angle XRQ ( angle 1)+Angle MQR(angle 2) = 180 degree
In other words Angle XRQ and Angle MQR are supplementary.
Now let us do a question
- In the figure given below AB ‖ CD and CD ‖ EF. Also EA is perpendicular to AB . If angle BEF = 55 degree. Find the values of x, y and z.
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