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If two lines intersect then the vertically opposite angles are equal - CBSE/Schools PDF Download
If two lines intersect each other, then the vertically opposite angles are ……….a)Equalb)Supplementaryc)Unequald)ComplementaryCorrect answer is option 'A'. Can you explain this answer?
Ref: https://edurev.in/question/492186/If-two-lines-intersect-each-other-then-the-vertically-opposite-angles-are-a-Equalb-Supplementaryc-
Given two lines AB and CD intersect each other at the point O.To prove: ∠1 = ∠3 and ∠2 = ∠4Proof:
From the figure, ∠1 + ∠2 = 180° [Linear pair] → (1)
∠2 + ∠3 = 180° [Linear pair] → (2)
From (1) and (2), we get
∠1 + ∠2 = ∠2 + ∠3
∴ ∠1 = ∠3
Similarly, we can prove ∠2 = ∠4 also.
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FAQs on If two lines intersect then the vertically opposite angles are equal - CBSE/Schools
| 1. What are vertically opposite angles? |  |
Ans. Vertically opposite angles are formed when two lines intersect. They are opposite to each other and share the same vertex. In other words, they are the angles that are opposite each other when two lines cross.
| 2. How are vertically opposite angles related to intersecting lines? | |
Ans. Vertically opposite angles are always equal when two lines intersect. This means that if two lines intersect at a point, the angles opposite to each other are of the same measure.
| 3. Why are vertically opposite angles important in geometry? | |
Ans. Vertically opposite angles play a significant role in geometry as they help establish relationships between different angles formed by intersecting lines. Their equality can be used to solve various geometric problems and prove theorems.
| 4. Can vertically opposite angles be of different measures? | |
Ans. No, vertically opposite angles are always equal. This property holds true regardless of the measure of the angles or the orientation of the intersecting lines.
| 5. How can we use the concept of vertically opposite angles in real-life situations? | |
Ans. The concept of vertically opposite angles can be applied in various real-life situations involving intersecting lines. For example, it can be useful in architecture and construction to ensure that lines intersect at accurate angles, or in navigation to determine the direction of two intersecting paths.
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Nov 24, 2024 Last updated |
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