6th Grade > Mathematics
UNDERSTANDING ELEMENTARY SHAPES MCQs
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Visualisation: 1 Mark
Finding the angle: 1 Mark
Type of Triangle: 1 Mark
The minute hand covers an angle of 30∘ in every five minutes. The angle covered in moving from 4 to 6 is 60∘.
The length of the minute hand remains constant. So the two sides of the triangle will be equal.
So the angles will be same for the sides which are equal.
Now, the angle included between the sides whose length are equal is 60∘.
So the other angles are (180-60)÷2 = 60∘.
Hence all the angles of the triangle are 60∘.
∴ The the triangle formed is an equilateral triangle.
Given in a clock, the hour hand is fixed at 12 and the minute hand is made to rotate. The reading of the angle moved by minute hand is taken as twice its actual reading. If the minute hand is at 6 according to the wrong reading, what is the position of minute hand according to the actual reading? Also, find the actual angle rotated by the minute hand. [4 MARKS]
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Steps: 2 Marks
Actual Reading: 1 Mark
Angle Rotated: 1 Mark
The minute hand when points at 6 cover an angle of 180 degrees.
As per question reading of the minute hand moved is twice the actual reading.
So, it will be pointing at 3.
Now for every five minutes, the minute hand would rotate through 30∘.
So when the minute hand passes from 12 to 3, total minutes passed =15.
Therefore the actual angle rotated by the minute hand = 3×30 = 90∘
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Each option: 1 Mark
(a) A sweet laddu is Spherical in shape.
(b)A road-roller is Cylindrical in shape.
(c)A Matchbox is in the shape of a Cuboid.
(d) A brick is in the shape of a Cuboid.
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Steps: 2 Marks
Answer: 1 Mark
Given that:
ABCD is a rectangle.
E and F are the mid-points of the lines AC and BD respectively.
∴AE=BF=EC=FD
Also, AH=HB=CG=GD [ H is mid point of AB , G is midpoint of CD ]
∠A, ∠B, ∠C and ∠D are right angles.
The four sides of rectangle formed i.e. EHFG will have equal dimensions.
∴The length of all their diagonals will also be same.
EH=HF=FG=EG
All sides of the quadrilateral are equal.
So either it will be a Rhombus or a Square.
But for both of these quadrilaterals, the diagonals intersect at a right angle.
The angle formed between the diagonals is a right angle.
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Steps: 2 Marks
Answer: 1 Mark
The angle covered when the minute hand moves from 3 to 6 is 90 degrees.
Given that:
The sides of the quadrilateral are equal.
So the quadrilateral can either be a rhombus or a Square.
But the angles included between the sides is 90∘.
∴ The quadrilateral is a Square.
Now in a square, the diagonals intersect each other at 90∘.
So angle between the diagonals is 90∘
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Definition: 1 Mark
Difference: 1 Mark
Each Point: 1 Mark
A line segment is a line which is contained between two points. The length of the line segment is fixed.
While a line has no ends and it is denoted with an arrow at both the ends.
a. In the given figure five points A, B, C, D, and E are marked.
b. In the given figure there are ten line segments AB, AD, AE, AC, BD, BE, BC, DE, DC and EC.
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Solutions: 1 Mark each
a) The length of all sides of the triangle is equal.
So it is an equilateral triangle.
b) In this triangle two sides are=6m
So it is an isosceles triangle.
c) In this triangle one of the angles is 90∘, so the triangle is a right-angled triangle.
d) In this triangle, two angles are equal to 70∘.So it is an isosceles triangle.
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Fractions: 1 Mark each
We may observe that in one complete clockwise revolution, the hour hand will rotate through 360∘
a) We have to find out the fraction of a clockwise revolution that an hour hand turns through when it rotates from 3 to 6.
Now, when the hour hand rotates from 3 to 6 it will rotate through 1 right angle.
∴ The fraction of revolution = 90∘360∘ = 14 revolution
b) Here the hour hand rotates from 6 to 12, which is to right angles.
∴ The fraction of revolution = 180∘360∘ = 12 revolution
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Triangle: 2 Marks
Given that:
The sum of two angles of the triangle is 90∘.
We know that the sum of all the three angles in a triangle is 180∘.
∴ The other angle = 180-90 = 90∘
Now we know that if one of the angles in a triangle is 90∘, then the triangle is a right-angled triangle.
Hence, the given triangle is a right-angled triangle.