Answer:
Step-by-step explanation:
The corresponding angles bisectors of two parallel lines are parallel
. A------------------------------B
. \. /
. \ /
. \. /.
C........D
Prove that the angle bisector of angle ECF is parallel to the angle bisector of angle EDF.
Proof :
Given that line AB is parallel to line CD.
When a transversal line EF intersects two parallel lines AB and CD ,it creates a set of corresponding angles.
Let angle EFC be one of the corresponding angles formed by the interesting lines . Let M be the midpoint of segments EF.
By the angle bisector theorem,the angle bisector of angle ECF passes through point M,the midpoint of EF.
Since AB is parallel to CD , angle ECF and angle EDF are alternate interior angles.
By the properties of alternate interior angles.
By the properties of alternate interior angles, angle ECF is congruent to angle EDF.
By the properties of alternate interior angles, angle ECF is congruent to angle EDF
Therefore, angle bisector of angle EDF also passea through point M the midpoint of M
Two lines that pass through the same point and are parallel to the same line are themselves parallel
Hence , the angle bisectors of angle ECF and EDF are parallel
Therefore , we have proved that the corresponding angles bisectors of two parallel lines are parallel.
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https://brainly.in/question/57339484?
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Answers & Comments
Answer:
Step-by-step explanation:
The corresponding angles bisectors of two parallel lines are parallel
. A------------------------------B
. \. /
. \. /
. \ /
. \. /
. \ /
. \ /
. \ /
. \. /
. \. /
. \. /
. \. /
. \. /
. \. /
. \. /
. \. /.
. \. /
. \. /
. \. /
. \. /
C........D
Prove that the angle bisector of angle ECF is parallel to the angle bisector of angle EDF.
Proof :
Given that line AB is parallel to line CD.
When a transversal line EF intersects two parallel lines AB and CD ,it creates a set of corresponding angles.
Let angle EFC be one of the corresponding angles formed by the interesting lines . Let M be the midpoint of segments EF.
By the angle bisector theorem,the angle bisector of angle ECF passes through point M,the midpoint of EF.
Since AB is parallel to CD , angle ECF and angle EDF are alternate interior angles.
By the properties of alternate interior angles.
By the properties of alternate interior angles, angle ECF is congruent to angle EDF.
By the properties of alternate interior angles, angle ECF is congruent to angle EDF
Therefore, angle bisector of angle EDF also passea through point M the midpoint of M
Two lines that pass through the same point and are parallel to the same line are themselves parallel
Hence , the angle bisectors of angle ECF and EDF are parallel
Therefore , we have proved that the corresponding angles bisectors of two parallel lines are parallel.
To know more about this
https://brainly.in/question/57339484?