If two lines intersect, prove that the vertically opposite angles are equal
Solution:
Consider two lines AB and CD which intersect at O.
We have to prove that the vertically opposite angles are equal
∠AOC = ∠DOB
∠AOD = ∠BOC
Consider ray OA that stands on the line CD
We know that the linear pair of angles is equal to 180 degrees.
∠AOC + ∠AOD = 180° ----------------------------- (1)
Consider ray OD that stands on the line AB
∠AOD + ∠DOB = 180° ----------------------------- (2)
Considering ray OB that stands on the line CD
∠DOB + ∠BOC = 180° ----------------------------- (3)
From (1) and (2),
∠AOC + ∠AOD = ∠AOD + ∠DOB
Canceling common term,
∠AOC = ∠DOB
From (2) and (3),
∠AOD + ∠DOB = ∠DOB + ∠BOC
Canceling common term,
∠AOD = ∠BOC
Therefore, the vertically opposite angles are equal.
✦ Try This: In the given l∥m. Find the value of 'a'
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.4 Problem 1
If two lines intersect, prove that the vertically opposite angles are equal
Summary:
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. It is proven that the vertically opposite angles are equal
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