state weather each pair of dotted lines in the following diagram are parallel or not parallel .Give reasons.
Answers
In the following diagram the figure (v), (vi) & (vii) are parallel and figure(iv) is not parallel.
Step-by-step explanation:
Referring to the figure attached below the reasons for each of the figures in the diagram whether the dotted lines are parallel or not parallel is as follows:
Property of angle associated with parallel lines: If two lines are parallel and transverse is drawn intersecting them then the pair of corresponding angles are equal.
Figure (iv):
Angle 1 = 180° – 91° = 89°
But here angle 1 is not equal to 99°.
∴ The dotted lines are not parallel.
Figure (v):
Angle 1 = 180° - 50° = 130°
Here, in this case, angle 1 is equal to the given corresponding angle of 130°.
∴ The dotted lines are parallel.
Figure (vi):
Angle 1 = 180° – 100° = 80°
Angle 2 = 180° - 100° = 80°
Angle 1 = angle 2 and from the figure (vi) we can see that they are pair of corresponding angles.
∴ The dotted lines are parallel.
Figure (vii):
Angle 1 = 180° - 120° = 60°
Here angle 1 is equal to the given corresponding angle of 60°.
∴ The dotted lines are parallel.
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Answer:
state weather each pair of dotted lines in the following diagram are parallel or not parallel give reasons