Class 7 Math Solution WBBSE Geometry Chapter 6 Parallel Lines And Transversal Exercise 6 Solved Problems
Parallel lines:
If two straight lines on the same plane do not intersect when produced in any direction, the two straight lines are said to be parallel to one another.
In the adjacent image, the straight lines AB, CD, and EF are parallel to each other i.e., AB || CD || EF
Transversal:
If a straight line intersects two or more straight lines in different points then the straight line is called a transversal of the lines.
In the adjacent image, the straight line EF intersects the straight lines AB and CD at points G and H respectively. So EF is called the transversal of lines AB and CD.
Vertically opposite angles:
If two straight lines intersect at a point, the angles formed on the opposite sides of the common point (vertex) are called vertically opposite angles.
In the adjacent image, two straight lines AB and CD intersect at O. ∠AOC and ∠BOD are two vertically opposite angles. Also, ∠AOD and ∠BOC are two vertically opposite angles.
Interior angles and exterior angles:
In the adjacent image ∠3, ∠4, ∠5, and ∠6 are interior angles whereas ∠1, ∠2, ∠7, and ∠8 are exterior angles.”
Corresponding angles:
Two angles lying on the same side of the transversal are known as corresponding angles if both lie either above are below the two given lines.
Alternate angles:
The pair of interior angles on the opposite side of the transversal are called alternate angles.
In the adjacent image, there are four pairs of corresponding angles. (∠1, ∠5), (∠2, ∠6), (∠8, ∠4), and (∠7, ∠3). There are two pairs of alternate angles (∠4,∠6) and (∠3, ∠5).
If a straight line intersects two parallel lines then the measurement of each pair of corresponding angles are equal and the measurement of alternate angles are equal.
Hence, ∠AGE = ∠GHC, ∠CHF = ∠AGH, ∠DHF = ∠BGH and ∠EGB = ∠GHD
Again, ∠AGH = ∠GHD and ∠BGH = ∠GHC
[The sum of the measurement of two interior angles in the same side of the transversal is 180°]
WB Class 7 Math Solution Parallel Lines And Transversal
Parallel Lines And Transversal Exercise 6
When the lines not parallel
When the lines are parallel
Lines are not parallel:
Lines are parallel:
