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.
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
In the below fig, lines �1 and �2 intersect at O, forming angles as shown in the figure. If x = 45, Find the values of x, y, z and u.
Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.
In the below fig, rays AB and CD intersect at O
Determine x when y =40
If l, m, n are three lines such that l || m and n ⊥ l, prove that n ⊥ m.
In the given figure, the value of y is
In the given figure, which of the following statements must be true?
(i) a + b = d + c
(ii) a + c + e = 180°
(iii) b + f = c + e
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =
Give two examples of perpendicular lines you can see in your environment.
Mention two real life situations where we use parallel lines
Two lines in a plane which do not meet at a point anywhere are called ______ lines.
