Advertisements
Advertisements
प्रश्न
If one of the four angles formed by two intersecting lines is a right angle, then show that
each of the four angles is a right angle.
Advertisements
उत्तर
Given,
AB and CD are two lines intersecting at O such that
`∠`BOC = 90°
`∠`AOC = 90°, `∠`AOD = 90° and `∠`BOD = 90°
Proof:
Given that `∠`BOC = 90°
Vertically opposite angles are equal
`∠`BOC = `∠`AOD = 90°
`∠`AOC, `∠`BOC are Linear pair of angles
`∠`AOC + `∠`BOC = 180° [LinearPair]
⇒`∠`AOC + 90° = 180°
⇒ `∠`AOC = 90°
Vertically opposite angles
∴ `∠`AOC = `∠`BOD = 90°
Hence, `∠`AOC = `∠`BOC = `∠`BOD = `∠`AOD = 90°
APPEARS IN
संबंधित प्रश्न
Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.
Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =
Consider the following statements:
When two straight lines intersect:
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are supplementary
Of these statements
In the given figure, AOB is a straight line. If ∠AOC + ∠BOD = 85°, then ∠COD =
In the given figure, the value of y is
Give two examples of perpendicular lines you can see in your environment.
Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.
Two parallel lines meet each other at some point.
Two lines in a plane which do not meet at a point anywhere are called ______ lines.
In the example of a 'Zebra crossing,' what feature specifically exemplifies the constant distance property of parallel lines?
