Class 9
1. Explain Euclid defination , axioms and postulates with suitable 2 examples .
2. Explain. equivalent versions of Euclid fifth postulate with suitable 2 examples .
3. Explain
Postulate 1
Postulate 2
Postulate 3
Postulate 4
Postulate 5
Explain clearly
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Answers
☆ ANSWER ☆:-
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1. Euclid was a Greek mathematician known for his contributions to geometry. ... Greek mathematician who applied the deductive principles of logic to geometry, thereby deriving statements from clearly defined axioms. His Elements remained influential as a geometry textbook until the 19th century.
Examples of axioms can be 2+2=4, 3 x 3=4 etc. In geometry, we have a similar statement that a line can extend to infinity. This is an Axiom because you do not need a proof to state its truth as it is evident in itself.
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2. Equivalent Versions of Fifth Postulate:-
“If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.”
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3. Postulate – I
A straight line segment can be formed by joining any two points in space.
In Geometry, a line segment is a part of a line that is bounded by 2 distinct points on either end. It consists of a series of points bounded by the two endpoints. Thus a line segment is measurable as the distance between the two endpoints. A line segment is named after the two endpoints with an overbar on them.
Postulate – II
Any straight line can be extended indefinitely on both sides. Unlike a line segment, a line is not bounded by any endpoint and so can be extended indefinitely in either direction. A line is uniquely defined as passing through two points which are used to name it.
Postulate – III
A circle can be drawn with any centre and any radius. For any line segment, a circle can be drawn with its centre at one endpoint and the radius of the circle as the length of the line segment. Consider a line segment bounded by two points. If one of these points is taken as the centre of a circle and the radius of the circle is taken as equal to the length of the segment, a circle can be drawn with its diameter twice than the length of the line segment.
Postulate – IV
All right angles are congruent or equal to one another. A right angle is an angle measuring 90 degrees. So, irrespective of the length of a right angle or its orientation all right angles are identical in form and coincide exactly when placed one on top of the other.
Postulate – V
Two lines are parallel to each other if they intersect the third line and the interior angle between them is 180 degrees.
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- I Hope it's Helpful My Friend.
Step-by-step explanation:
1A:-
A non-ideal solution is a solution whose properties are generally not very predictable on account of the intermolecular forces between the molecules. None. Non-ideal solutions by definition cannot be dealt with through Raoult's Law. Raoult's Law is strictly for ideal solutions only.
A solution shows positive deviation from ideal behaviour when the interaction between them, unlike molecules, is weaker than the like molecules i.e interaction between A-B molecules is weaker than A-A and B-B molecules. In this case, the molecules find it more easy to escape an thus the vapour pressure of the solution is higher than expected. Example, when acetone is mixed with ethanol, energy, is required to break hydrogen bonds between ethanol molecules.
2A:-
The two equivalent versions of Euclid's fifth postulate are,
1. For every line and for every point not lying on , there exists a unique line passing through and parallel to .
2. Two distinct intersecting lines cannot be parallel to the same line.
3A:-
a, Postulates of Dalton’s atomic theory:
(1) All the matter is made up of very small particles called ‘atoms’.
(2) Atoms cannot be divided.
(3) Atoms can neither be created nor be destroyed.
(4) Atoms are of various kinds. There are as many kinds of atoms as are elements.
(5) All the atoms of a given element are identical in every respect, having the same mass, size and chemical properties.
(6) Atoms of different elements differ in mass, size and chemical properties.
(7) The ‘number’ and ‘kind’ of atoms in a given compound is fixed.
(8) During chemical combination, atoms of different elements combine in small whole numbers to form compounds.
(9) Atoms of the same elements can combine in more than one ratio to form more than one compound.
(b) The postulate “The elements consists of atoms and that atoms can neither be created nor destroyed” can be used to explain the law of conservation of mass.
(c) The postulate “The elements consist of atoms having fixed mass, and that the number and kind of atoms of each element in a given compound is fixed” can be used to explain the law of constant proportions.