Which of the following statements are true and which are false? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are an infinite number of lines which pass through two distinct points. (iii) A terminated line can be produced indefinitely on both the sides. (iv) If two circles are equal, then their radii are equal. (v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

1. Which of the following statements are true and which are false? Give reasons for

your answers.

(i) Only one line can pass through a single point.

(ii) There are an infinite number of lines which pass through two distinct points.

(iii) A terminated line can be produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

Answer:

(i)False.

Correct statement

Through a single point, infinite number of lines can pass. 

In above figure, you can see that there are infinite numbers of lines can pass through a single point S.

(ii) False.

Correct statement

through two distinct points, only one line can pass.

In above figure, it can see that there is only one single line that drawn through two

Distinct points R and S

.

(iii) True.

According to Euclid’s laws, A terminated line can be produced indefinitely on both the sides. 

In above figure, you can see there are indefinitely lines both side

(iv)True.

According to axioms 4 of the Euclid, If two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal.

In above figure, it can see both circle have equal radius  

(v) True.

According to Euclid’s axiom first, things which are equal to the same thing,

And in our given problem it is given that AB and XY are two terminated lines and both are equal to a third line PQ are equal to one another. Therefore, the lines AB and XY will be equal to each other.

Euclid’s Definitions axioms postulates

Introduction
The word ‘geometry’ comes form the Greek words ‘geo’, meaning the ‘earth’, and ‘metrein’, meaning ‘to  measure’. Pythagoras and his group discovered many geometric properties and developed the theory of  geometry to a great extent. This process continued till 300 BC. At that time Euclid, a teacher of mathematics  at Alexandria in Egypt, collected all the known work and arranged it in his famous treatise,

Euclid’s Definitions
He began his exposition by listing 23 definitions in Book 1 of the ‘Elements’ 7 definitions are given below 
1. A point is that which has no part.
2. A line is breadthless length.
3. The ends of a line are points.
4. A straight line is a line which lies evenly with the points on itself.
5. A surface is that which has length and breadth only.
6. The edges of a surface are lines.
7. A plane surface is a surface which lies evenly with the straight lines on itself.
Euclid’s axioms
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal.
(3) If equals are subtracted from equals, the remainders are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things which are halves of the same things are equal to one another.
Euclid’s five postulates
Postulate 1 : A straight line may be drawn from any one point to any other point.
Postulate 2 : A terminated line can be produced indefinitely.
Postulate 3 : A circle can be drawn with any centre and any radius.
Postulate 4 : All right angles are equal to one another.
Postulate 5 : 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.
Theorem 5.1 : Two distinct lines cannot have more than one point in common.
Proof : Here we are given two lines l and m. We need to prove that they have only one point in common.
For the time being, let us suppose that the two lines intersect in two distinct points, say P and Q. So, you have two lines passing through two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct points. So, the assumption that we started with, that two lines can pass through two distinct points is wrong. From this, what can we conclude? We are forced to conclude that two distinct lines cannot have more than one point in common.
Equivalent Versions of Euclid’s Fifth Postulate
‘For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l’.
Summary

In this chapter, you have studied the following points:
1. Though Euclid defined a point, a line, and a plane, the definitions are not accepted by
mathematicians. Therefore, these terms are now taken as undefined.
2. Axioms or postulates are the assumptions which are obvious universal truths. They are not
proved.
3. Theorems are statements which are proved, using definitions, axioms, previously proved
statements and deductive reasining.
4. Some of Euclid’s axioms were :
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal.
(3) If equals are subtracted from equals, the remainders are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things which are halves of the same things are equal to one another.
5. Euclid’s postulates were :
Postulate 1 : A straight line may be drawn from any one point to any other point.
Postulate 2 : A terminated line can be produced indefinitely.
Postulate 3 : A circle can be drawn with any centre and any radius.
Postulate 4 : All right angles are equal to one another.
Postulate 5 : 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.
6. Two equivalent versions of Euclid’s fifth postulate are:
(i) ‘For every line l and for every point P not lying on l, there exists a unique line m
passing through P and parallel to l’.
(ii) Two distinct intersecting lines cannot be parallel to the same line.
7. All the attempts to prove Euclid’s fifth postulate using the first 4 postulates failed. But they
led to the discovery of several other geometries, called non-Euclidean geometries.

.	Maths class 9 Introduction to Euclid’s Geometry
.	Definitions, formula and notes of  Euclid’s Geometry
.	Introduction , Indian contribution in geometry ,Euclid’s Definitions, Euclid’s axioms, Euclid’s five postulates
.	Theorem 5.1 : Two distinct lines cannot have more than one point in common.
.	Equivalent Versions of Euclid’s Fifth Postulate
.
.	Ncert Solution Exercise 5.1
1	Which of the following statements are true and which are false? Give reasons for youranswers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A terminated line can be produced indefinitely on both the sides.(iv) If two circles are equal, then their radii are equal.(v) In Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.
2	Give a definition for each of the following terms. Are there other terms that need to bedefined first? What are they, and how might you define them?(i) parallel lines (ii) perpendicular lines (iii) line segment(iv) radius of a circle (v) square
3	Consider two ‘postulates’ given below:(i) Given any two distinct points A and B, there exists a third point C which is inbetween A and B.(ii) There exist at least three points that are not on the same line.Do these postulates contain any undefined terms? Are these postulates consistent?Do they follow from Euclid’s postulates? Explain.
4	If a point C lies between two points A and B such that AC = BC, then prove thatAC = 1/ 2 AB. Explain by drawing the figure.
5	In Question 4, point C is called a mid-point of line segment AB. Prove that every linesegment has one and only one mid-point.
6	In Fig. 5.10, if AC = BD, then prove that AB = CD.
7	Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note thatthe question is not about the fifth postulate.)
	Ncert Solution Exercise 5.2
1	How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
2	Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

electrochemistry formulas

Formula of rate of appearance
Average rate of reaction
Instantaneous rate of reaction  

rate of appearance average rate of reaction instantaneous rate and rate law of reaction

Formula of first order reaction  

formula of first order reaction 

Arrhenius equation all formulas

All formula of Arrhenius equation 

 Table of rate constant 

Table of formula of rate constant 

Formula of zero order reaction 

Formula of zero order reaction 

What is the difference between the manner in which movement takes place in a sensitive plant and the movement in our legs

Q. No. 12: What is the difference between the manner in which movement takes place in a sensitive plant and the movement in our legs?

Ans:

	Movement in sensitive plants		Movement in our legs
1	The movement in a sensitive plant is a response to stimulus(touch) which is a involuntary action.	1	Movement in our legs is a voluntary action.
2	No special tissue is there for the transfer of information	2	A complete system CNS and PNS is there for the information exchange.
3	Plant cells do not have specialised protein for movements.	3	Animal cells have specialised protein which help muscles to contract.

Compare and contrast nervous and hormonal mechanisms for control and coordination in animals

Q. No. 11:Compare and contrast nervous and hormonal mechanisms for control and coordination in animals.

Ans:

	Nervous control		Hormonal Control
1	It is consist of nerve impulses between PNS, CNS and Brain.	1	It consists of endocrine system which secretes hormones directly into blood.
2	Here response time is very short.	2	Here response time is very long.
3	Nerve impulses are not specific in their action.	3	Each hormone has specific actions.
4	The flow of information is rapid.	4	The flow of information is very slow.

How are involuntary actions and reflex actions different from each other

Q. No. 10: How are involuntary actions and reflex actions different from each other?

Ans:

Involuntary action is the set of muscle movement which do not require thinking. But it is controlled by brain for example beating of heart beat.

While on the other hand, the reflex action is rapid and spontaneous action in response to any stimulus. For example closing of eyes immediately when bright light is focused.

What is the need for a system of control and coordination in an organism

Q. No. 9: What is the need for a system of control and coordination in an organism?

Ans:  There are various organs in an organism. These organs must be carefully controlled and coordinated for the survival of an organisms. In the body of an organism various fluids are secreted from the glands of the endocrine system. These hormones are responsible for the overall growth and development of an organism. All others daily decision that includes voluntary and involuntary action are controlled by central nervous system(CNS). 

How does chemical coordination occur in plants

Q. No. 8: How does chemical coordination occur in plants?

 Ans: Chemical coordination in plants are occurred in plants with the help of fluids secreted in plants known as phytohormones or plant hormones. These hormones regulate the growth of the plants. For example auxin responsible for the growth of the plants and the Cytokinin helps in cell division in the fast growing part of the plant such as plant hormones.

Which signals will get disrupted in case of a spinal cord injury

Q. No. 7:  Which signals will get disrupted in case of a spinal cord injury?

Ans: In case of the spinal cord injury, the signals coming from the nerves as well as the signals coming to the receptors will be disrupted. As both these signals meet in a bundle in spinal cord so there is any spinal cord injury then both these signals are disrupted.