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Write whether the following statements are true or false. In each case justify your answer.
The Euclidean geometry is used only for figures in the plane.
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True, It fails on the curved surfaces. For example on curved surfaces, the sum of angles of a triangle may be move than
Write whether the following statements are true or false. In each case justify your answer.
The boundaries of the solids are curves.
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False, Because the boundaries of the solids are surfaces.
Write whether the following statements are true or false. In each case justify your answer.
The edges of a surface are curves.
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False, Because the edges of surfaces are lines.
Write whether the following statements are true or false. In each case justify your answer.
In geometry, we take a point, a line and a plane as undefined terms.
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True, To define a point, a line and a plane in geometry we need to define may other things
Write whether the following statements are true or false. In each case justify your answer.
Euclid’s fourth axiom says that everything equals itself.
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True, It is the justification of the principle of super position
A and B have the same weight. If they each gain weight by 2 kg, how will their new weights be compared ?
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Their new weight will remain the same.
Let A weight be kg and B weight = kg
Why Euclidean geometry is not applicable to a triangle drawn on a sphere ?
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Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere.
A square is a polygon made up of four line segments, out of which length of three line segments are equal to the length of fourth one and all its angles are right angles. Define the terms used in this definition which you feel necessary. Are there any undefined terms?
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Polygon – A simple closed figure made up of 3 or more line segments.
linesegment – Part of a line with two and points
line – undefined term
Point – undefined term
Angle – A figure formed by two rays with a common initial point
Ray – Part of a line with one end point
Right angle – Angle whose measure is
Check whether the following system of axioms is consistent or inconsistent.
(i) Things which are equal to the same thing are equal to one another.
(ii) If equals are added to equals, the wholes are equal.
(iii) Things which are double of the same thing are equal to one another.
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(I) Consistent – This statement is Euclid first axiom
(II) Consistent – This statement is Euclid second axiom
(III) Consistent – This statement is Euclid third axiom
Check whether the following system of axioms is consistent or inconsistent.
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.
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(I) Inconsistent – It is a theorem not a axiom
(II) Consistent – It is true and also an axiom
State the axiom used in each of the following :
For the given figure :
(i) AD + DB = AB
(ii) \(\angle \)ADC + \(\angle \)BDC = \(\angle \)ADB
(iii) \(\angle \)ADC + \(\angle \)BDC = \(\angle \)ADB
(iv) \(\angle \)ACB > \(\angle \)DCB
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(i) Things which coincide with one another are equal to one another
(ii) The whole is greater than part
(iii) The whole is greater than part
(iv) The whole is greater than part