Answer:
yes these are equal because ,
by angle sum property
(angles of a triangle is equal to 180°
Step-by-step explanation:
let AB and CD be two lines intersecting at O . 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.
Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)
We can write ∠ AOD + ∠ BOD = 180° (Linear pair axiom)……………(2)
From (1) and (2), we can write
∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD
This implies that ∠ AOC = ∠ BOD
Therefore it is proved lines intersect each other then the vertically opposite angles are equal.
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Answers & Comments
Answer:
yes these are equal because ,
by angle sum property
(angles of a triangle is equal to 180°
Proof of two lines intersect each other then the vertically opposite angles are equal
Step-by-step explanation:
let AB and CD be two lines intersecting at O . 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.
Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)
We can write ∠ AOD + ∠ BOD = 180° (Linear pair axiom)……………(2)
From (1) and (2), we can write
∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD
This implies that ∠ AOC = ∠ BOD
Therefore it is proved lines intersect each other then the vertically opposite angles are equal.