Question

Draw rough diagrams of two angles such that they have

(a) One point in common

(b) Two points in common

(c) Three points in common

(d) Four points in common

(e) One ray in common

Answer 1

Consider fig. 1 shown below. An angle has two rays $\overrightarrow{BA}$ and $\overrightarrow{BC}$. Here, one common point is $B$.

Hence, one point is common.

(a)If two angles have a common point, then their end point is the same. Consider fig 2 as shown below. Here, $\angle ABC$ and $\angle DBA$ have $1$ common point $B$.

(b)Since, an angle has only one end point, we cannot have two angles with two points in common. It is not possible.

(c) Since, an angle has only one end point, we cannot have two angles with three points in common. It is not possible.

(d) Since, an angle has only one end point, we cannot have two angles with four points in common. It is not possible.

(e) Consider fig 3 shown below. Here, $\angle ABC$ and $\angle EBC$ have ray $\overrightarrow{BC}$ in common.