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Maths 5 Marks Questions

Practical Geometry Symmetry and Visualising Solid Shapes · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 4 questions.

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5 Marks Questions

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

Question 15 Marks
Construct a right-angled triangle whose hypotenuse measures $5\ cm$ and one of the other sides measures $3.2\ cm.$
Answer
The steps are as follows:
Step I: Draw a line $AB$ of side $3.2cm$
Step II: Construct $90^\circ $ at point $B$ and draw a straight line through it.
Step III: From point $A$ cut an arc at $90^\circ $ line of length $5cm.$​​​​​​​
Step IV: The point where arc intersect with $90^\circ $ line is the third point of triangle, $C.$​​​​​​​
Step V: Join $AC$ to complete the triangle.
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Question 25 Marks
Which of the figures given below have both line and rotational symmetry?
$a.$

$b.$

$c.$

$d.$
Answer
Only $(a)$ and $(c)$ have both line and rotational symmetry. In the given figure, line of symmetry will be shown as
Also, rational symmetry will be shown as

$\frac{360^\circ}{8}=45^\circ, i.e.$ rational angle is equal to $45^\circ $. In the given figure, line of symmetry will be shown as
Also, rational symmetry will be shown as

$\frac{360^\circ}{10}=36^\circ, i.e.$ rational angle is equal to $36^\circ .$
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Question 35 Marks
Draw an isosceles triangle with each of equal sides of length 3cm and the angle between them as $45^\circ .$
Answer

The steps are as follows:
Step I: Draw a line $AB$ of side $3cm$
Step II: Construct $45^\circ $ at point $B$ and draw a straight line through it. $45^\circ $ angled line can be constructed by taking same distance from B towards $A [X]$ and towards the $90^\circ [Y]$ line. Then cut the arc from the two points.
Step III: From point $B$ cut an arc at $45^\circ $ line of length $3cm.$
Step IV: The point where arc intersect with $90^\circ $ line is the third point of triangle, $C.$
Step V: Join $AC$ to complete the triangle.
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Question 45 Marks
Construct an equilateral triangle $ABC$ of side $6\ cm.$
Answer

The steps are as follows:
Step I: Draw a line $AB$ of side $6\ cm.$
Step II: From $B$ draw an arc with a radius of $6\ cm.$
Step III: From $A$ draw an arc with a radius of $6\ cm.$
Step IV: The point where the two arc intersects is the third point of triangle, $C.$
Step V: Join $AC$ to complete the triangle.
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