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
In the below fig, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ − 5 : 7,
find all the angles.
In the below fig, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.
Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.
In the given figure, the value of y is
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =
Look at the picture given below. Decide whether the lines given in picture is parallel or perpendicular to each other and write the answer in the box.
Mention two real life situations where we use parallel lines
Which phrase correctly describes the distance between two parallel lines?
In the example of a 'Zebra crossing,' what feature specifically exemplifies the constant distance property of parallel lines?
If the shortest distance between two straight lines in a plane is observed to change, what must be true about the lines?
