Introduction to Euclids Geometry Maths - Introduction to Euclids Geometry

Write the correct answer in the following:
Thales belongs to the country:

1. Babylonia.
2. Egypt.
3. Greece.
4. Rome.

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Greek’s emphasised on:

1. Inductive reasoning.
2. Deductive reasoning.
3. Both A and B.
4. Practical use of geometry.

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Pythagoras was a student of:

1. Thales.
2. Euclid.
3. Both A and B.
4. Archimedes.

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Euclid divided his famous treatise “The Elements” into:

1. 13 chapters.
2. 12 chapters.
3. 11 chapters.
4. 9 chapters.

Write the correct answer in the following:
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio:

1. 1 : 3 : 4
2. 4 : 2 : 1
3. 4 : 4 : 1
4. 4 : 3 : 2

Write whether the following statements are True or False? Justify your answer:
The statements that are proved are called axioms.

Write whether the following statements are True or False? Justify your answer:
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Write whether the following statements are True or False? Justify your answer:
Two distinct intersecting lines cannot be parallel to the same line.

Write whether the following statements are True or False? Justify your answer:
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l” is known as Playfair’s axiom.

Write whether the following statements are True or False? Justify your answer:
The boundaries of the solids are curves.

Study the following statement:
"Two intersecting lines cannot be perpendicular to the same line". Check whether it is an equivalent version to the Euclid’s fifth postulate.
[Hint: Identify the two intersecting lines l and m and the linen in the above statement]

In the we have AB = BC, BX = BY. Show that AX = CY.

Solve the following question using appropriate Euclid’s axiom:
It is known that x + y = 10 and that x = z. Show that z + y = 10?

In the we have AC = DC, CB = CE. Show that AB = DE.

Read the following 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. Things which are double of the same thing are equal to one another.

Check whether the given system of axioms is consistent or inconsistent.

In the we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Solve the following question using appropriate Euclid’s axiom:
Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.

Read the following statement:
An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle.

In the:

1. AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC.
2. BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.