In Geometry, lines can relate in a variety of ways, such as intersecting, and transverse.
Intersecting lines:
Two or more lines which are passing through a common point are called intersecting lines.
Transverse:
Many times we might have observed that some railway lines crossing many other lines. This gives the concept of transversal.
A transversal is a line which intersects two or more points at different points.
Angles made by a transversal:
If a transversal l cuts two lines a and b then 8 angles are formed at the intersection points. We have some particular names for the angles thus formed.
a) Interior angles:
The angles which are formed inside the lines a and b are called interior angles. Here, ∠3, ∠4, ∠5 and ∠6 are the interior angles.
b) Exterior angles:
The angles which are formed above the line a and below the line b are called the exterior angles. Here, ∠1, ∠2, ∠8 and ∠7 are the exterior angles.
c) Corresponding angles:
The angles which lie on the same relative position are called the corresponding angles.
Here, 1 &5, 2&6, 4&8 and 3&7 are the pairs of corresponding angles.
d) Alternate interior angles:
Interior angles which are on the opposite side of the transversal are called alternate interior angles. Here, ∠4&∠6 and ∠3&∠5 are the alternate interior angles.
e) Alternate exterior angles:
Exterior angles which are on the opposite side of the transversal are called alternate exterior angles. Here, ∠1&∠7 and ∠2&∠8 are the alternate exterior angles.
Transversal of parallel lines:
A transversal is a line cutting any two lines. But if a transversal cuts two parallel lines there are some pairs of angles which are equal and are stated as follows.
Here, the transversal is cutting two parallel lines and in this case,
a) Pairs of alternate interior angles measure same.
∠c = ∠f and ∠d = ∠e.
b) Pairs of exterior angles are same.
∠a = ∠h and ∠b = ∠g.
c) Pairs of corresponding angles are same.
∠a = ∠e , ∠b = ∠f, ∠c = ∠g and ∠d= ∠h.
d) Each pair of interior angles on the same side of the transversal are supplementary.
∠c+∠d = 1800 and ∠g+∠h = 1800.
Do you also need help with your Writing? Take a look at our Writing tutoring services.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Fredericton visit: Tutoring in Fredericton.