In Figure, if x + y = w + z, then prove that AOB is a line.
Solution and Explanation
It can be observed that, x + y + z + w then prove that AOB is a line.
\(⇒\)\(\text{ x+y+w+z = 360°}\)
It is given that,
\(\text{x+y = w+z}\)
So, (x + y) +(x + y) = 360°
2(x + y) = 360°
∴ (x + y) = 180°
Since x and y form a linear pair, AOB is a line.
Top Questions on Intersecting Lines and Non-intersecting Lines
- Q is a point on the line BD dividing the segment internally. AB, PQ and CD are drawn perpendicular to BD. If AB = a, PQ = b and CD = c, then
- AP POLYCET - 2019
- Mathematics
- Intersecting Lines and Non-intersecting Lines
- It is given that \( ∠\)XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects \(∠\)ZYP, find \(∠\)XYQ and reflex \(∠\)QYP.
- CBSE Class IX
- Mathematics
- Intersecting Lines and Non-intersecting Lines
- In Figure, lines AB and CD intersect at O. If \(∠\)AOC+\(∠\)BOE=70° and \(∠\)BOD=40°, find \(∠\)BOE and reflex \(∠\)COE.
- CBSE Class IX
- Mathematics
- Intersecting Lines and Non-intersecting Lines
- In Figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that \(∠\)ROS = \(\frac{1}{2}\) (\(∠\)QOS – \(∠\)POS)
- CBSE Class IX
- Mathematics
- Intersecting Lines and Non-intersecting Lines
- In Figure, \(∠\)PQR = \(∠\)PRQ, then prove that \(∠\)PQS = \(∠\)PRT.
- CBSE Class IX
- Mathematics
- Intersecting Lines and Non-intersecting Lines
Questions Asked in CBSE Class IX exam
- Fig shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:
- Which of the three is travelling the fastest?
- Are all three ever at the same point on the road?
- How far has C travelled when B passes A?
- How far has B travelled by the time it passes C?
- CBSE Class IX
- Graphical Representation of Motion
- Factorise : (i) x3 – 2x 2 – x + 2 (ii) x 3 – 3x 2 – 9x – 5 (iii) x 3 + 13x 2 + 32x + 20 (iv) 2y 3 + y 2 – 2y – 1.
- CBSE Class IX
- Factorisation of Polynomials
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play
- CBSE Class IX
- The fun they had
- What are the main features of the mechanical teachers and the schoolrooms that Margie and Tommy have in the story?
- CBSE Class IX
- The fun they had
- A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period. (b) Which part of the graph represents uniform motion of the car?
- CBSE Class IX
- Graphical Representation of Motion