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MATHS 5 Marks Questions

Basic Geometrical Tools · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 3 questions.

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5 Marks Questions

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3 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
If $AB = 7.5\ cm$ and $CD = 2.5\ cm,$ construct a segment whose length is equal to:
$2AB + 3CD$
Answer
Given: $AB= 7.5\ cm$ and $CD = 2.5\ cm$ Draw $AB$ and $CD$

Draw a line/ and take point Eon it. Now, take a divider and open it such that the ends of both its arms are at $A$ and $B.$
Then, we lift the divider and place its one end at $E$ and other end (say $F$) on the line $1,$
as shown in the figure. Again, lift the divider and place its one end at $F$ and another end $(G)$ on the line $1,$ opposite to $E.$
Now, reset the divider in such a way that the ends of its one hand are at $C$ and the end of other hand is at $D.$
Then, we lift the divider and place its one end at $G$ and another end (say $H$) on the line $1,$
opposite to $E$ as shown in the figure.
Again, lift the divider and place its one end at $H$ and other end (say $I$) on the line $1,$
opposite to $E$ as shown in the figure.
Again, lift the divider and place its one end at $I$ and another end (say $J$) on the line $1,$
opposite to $E$ as shown in the figure.
$EG$ is required line segment, whose length is equal to $(2AB + 3CD).$​​​​​​​
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Question 25 Marks
Draw a line segment $CD.$ Produce it to $CE$ such that $CE = 3CD.$
Answer
We draw a line l and take two points $C$ and $D$ on it.
Take a divider and open it such that its end of both arms is at $C$ and $D.$
Then, we lift the divider and place its one end at $D$ and other end on the line $l$ opposite to $C$ as shown in the figure.
Let this point be $A.$
Lift the divider again and place its one end at $A$ and other end on the line $1$ opposite to $C.$
Name this point as $E.$
Here $CD = DE = AE$
Therefore, $CE = CD + DE + AE$
$= CD + CD + CD ($As, $CD ± DE = AE)$
or, $CE = 3CD$
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Question 35 Marks
Match the following statements:
  Column $A$   Column $B$
$i$ Line segment has $a$ at a point
$ii$ Two segments may intersect $b$ if they have equal lengths
$iii$ Two segments are congruent $c$ two end-point
$iv$ Line segment is $d$ portion of a line
Answer
  Column $A$   Column $B$
$i$ Line segment has $c$ two end$-$point
$ii$ Two segments may intersect $a$ at a point
$iii$ Two segments are congruent $b$ if they have equal lengths
$iv$ Line segment is $d$ portion of a line
Solution:
$i.\ $A line segment is a part of a line that is bounded by two distinct end points.

$ii.\ $Two line segments will either not intersect at all or intersect at one point. It can never intersect at more than one point.

$iii.\ $Line segments are congruent if they have the same lengths. If $AB = 6\ cm$ and $CD = 6\ cm$ Then, $AB$ and $CD$ are congruent.
$iv.\ $A line segment is a part of a line that is bounded by two distinct end points.
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