Basic Geometrical Ideas - Class 6 - Mathematics
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Exercise 4.1 - Basic Geometrical Ideas | NCERT | Mathematics | Class 6
Use the figure to name :
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
(a) $B$, $C$, $D$, $E$, and $O$ are five points.
(b) $\overline{BD}$ can be one such line.
(c) $\overrightarrow{OB}$, $\overrightarrow{OC}$, $\overrightarrow{OE}$, and $\overrightarrow{OD}$ are four such rays.
(d) $\overline{OB}$, $\overline{OC}$, $\overline{OE}$, $\overline{ED}$, and $\overline{BD}$, are five such line segments.
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
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Sign up nowUse the figure to name :
(a) Line containing point $\mathrm{E}$.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.
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Sign up nowHow many lines can pass through (a) one given point? (b) two given points?
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Sign up nowDraw a rough figure and label suitably in each of the following cases:
(a) Point $\mathrm{P}$ lies on $\overline{\mathrm{AB}}$.
(b) $\overleftrightarrow{\mathrm{XY}}$ and $\overleftrightarrow{\mathrm{PQ}}$ intersect at $\mathrm{M}$.
(c) Line $l$ contains $\mathrm{E}$ and $\mathrm{F}$ but not $\mathrm{D}$.
(d) $\overleftrightarrow{\mathrm{OP}}$ and $\overleftrightarrow{\mathrm{OQ}}$ meet at $\mathrm{O}$.
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Sign up nowConsider the following figure of line $\overrightarrow{\mathrm{MN}}$. Say whether following statements are true or false in context of the given figure.
(a) Q, M, O, N, P are points on the line $\overrightarrow{\mathrm{MN}}$.
(b) $\mathrm{M}, \mathrm{O}, \mathrm{N}$ are points on a line segment $\overline{\mathrm{MN}}$.
(c) $\mathrm{M}$ and $\mathrm{N}$ are end points of line segment $\overline{\mathrm{MN}}$.
(d) $\mathrm{O}$ and $\mathrm{N}$ are end points of line segment $\overline{\mathrm{OP}}$.
(e) $\mathrm{M}$ is one of the end points of line segment $\overline{\mathrm{QO}}$.
(f) $\mathrm{M}$ is point on ray $\overrightarrow{\mathrm{OP}}$.
(g) Ray $\overrightarrow{\mathrm{OP}}$ is different from ray $\overrightarrow{\mathrm{QP}}$.
(h) Ray $\overrightarrow{\mathrm{OP}}$ is same as ray $\overrightarrow{\mathrm{OM}}$.
(i) Ray $\overrightarrow{\mathrm{OM}}$ is not opposite to ray $\overrightarrow{\mathrm{OP}}$.
(j) $\mathrm{O}$ is not an initial point of $\overrightarrow{\mathrm{OP}}$.
(k) $\mathrm{N}$ is the initial point of $\overrightarrow{\mathrm{NP}}$ and $\overrightarrow{\mathrm{NM}}$.
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Sign up nowExtra Questions - Basic Geometrical Ideas | NCERT | Mathematics | Class 6
When three lines intersect each other at three different points, then how many angles will be formed?
A) 3
B) 6
C) 12
D) 24
When three lines, denoted as $AB$, $BC$, and $AC$, intersect at three distinct points $A$, $B$, and $C$, each intersection point creates four angles. This is evident from a typical geometric setup of three intersecting lines.
Angles formed at point (A): 4
Angles formed at point (B): 4
Angles formed at point (C): 4
Adding these together, the total number of angles created when the three lines intersect is: $$ 4 + 4 + 4 = 12 $$
Therefore, the total number of angles formed is 12.
The alphabet is an example of intersecting lines.
A $\mathrm{C}$
B $\mathrm{D}$
C $\mathrm{X}$
D $\mathrm{Q}$
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