Theorem 6.1 chapter 6 can study by students of class 9. These definitiona and formulas of Class 9 Maths Chapter 6: Lines and Angles is developed and witten by our expert teachers. Maths formulas. Theorem 6.1 is prepapred and collected from varius resources to help the students.
Theorem 6. 1 : If two lines intersect each other, then the vertically opposite angles are equal
Given :- two lines intersect each other
To prove :- ∠AOC = ∠BOD and ∠AOD = ∠BOC
Proof :- AB and CD be two lines intersecting at O as shown in Fig 6 8 They lead to two pairs of
vertically opposite angles, namely, (i) ∠AOC and ∠ BOD
(ii) ∠ AOD and ∠ BOC
We need to prove that ∠AOC = ∠BOD
and ∠AOD = ∠BOC
Now, ray OA stands on line CD
From (Linear pair axiom)
∠AOC + ∠AOD = 180° … (1)
∠AOD + ∠BOD = 180° … (2)
From (1) and (2), we can write
∠AOC + ∠AOD = ∠AOD + ∠BOD
This implies that ∠AOC = ∠BOD
Similarly, it can be proved that ∠AOD = ∠BOC
Parallel Lines and a Transversal
∠1, ∠ 2, ∠7 and ∠ 8 are called exterior angles,
∠ 3, ∠ 4, ∠ 5 and ∠6 are called interior angles
(a) Corresponding angles :
(i) ∠1 = ∠ 5 (ii) ∠ 2 = ∠ 6 (iii) ∠ 4 = ∠ 8 (iv) ∠ 3 = ∠ 7
(b) Alternate interior angles :
(i) ∠ 4 = ∠ 6 (ii) ∠ 3 = ∠ 5
(c) Alternate exterior angles:
(i) ∠1 = ∠ 7 (ii) ∠ 2 = ∠8
(d) Interior angles on the same side of the transversal:
(i) ∠4 + ∠5 =180°(ii) ∠3 + ∠ 6 =180°
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