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Introduction To Euclid’s Geometry

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 line n in the above
statement.]

Introduction To Euclid’s Geometry

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

Introduction To Euclid’s Geometry

Read the following statement:
“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 in this? Can you justify that all angles and sides of a square are equal?

Introduction To Euclid’s Geometry

It is known that x + y = 10 and that x = z. Show that z + y = 10?

Introduction To Euclid’s Geometry

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

Introduction To Euclid’s Geometry

Solve the equation a – 15 = 25 and state which axiom do you use here.

Introduction To Euclid’s Geometry

Ram and Ravi have the same weight. If they each gain weight by 2 kg, how will their new weights be compared ?

Introduction To Euclid’s Geometry

Write whether the following statement is 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.

Introduction To Euclid’s Geometry

Write whether the following statement is True or False? Justify your answer :

Two distinct intersecting lines cannot be parallel to the same line

Introduction To Euclid’s Geometry

Write whether the following statement is 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