1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# To divide a line segment PQ in a certain ratio, we draw a ray PM. Why don’t we draw it with an obtuse angle?

A

We cannot measure an obtuse angle with the given line segment.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

Drawing an obtuse angle would make my constructions very congested.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

The diagram would be very large.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

The textbook says we should draw an acute angle.

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B Drawing an obtuse angle would make my constructions very congested. Suppose we draw PM such that the angle ∠QPM is an obtuse angle. Next we mark (m+n) arcs on the ray PM such that PP1 = P1P2 = P2P3 = … = Pm+n−1Pm+n. For our convenience let us assume m+n=5 so we can explain things much easier. (In our case the required ratio could be 1:4 or 2:3 or 3:2 or 4:1 etc...) Now in the △QPP5, If, ∠QPP5 is obtuse then ∠QP5P and ∠PQP5 would become very small (compared to the case where ∠ QPP5 is acute) and it would be difficult to draw a line parallel to QP5 (Because small angles and hence small radii of arcs are involved in construction of parallel lines) This will make drawing of parallel lines very congested compared to drawing parallel lines on line segment PN with acute angle ∠QPN. You can see from the diagram that P4Q′∥P5Q is more closely spaced compared to P′4Q′∥P′5Q. So we prefer to draw an acute angle to make it more clear and spacious i.e. to avoid congestion.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Dividing a Line Segment
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program