Euclid's Elements of Geometry

Prove that things which are double of the same things are equal to one another.

Prove that two distinct lines have only one intersection point by Euclid's postulate.

Prove that an equilateral triangle can be constructed on any given line segment by using Euclid's $3^{\mathrm{rd}}$ postulate.

 If $A,B,C$ are collinear points on a line and $B$ lies between $A$ and $C$, then prove that $AC-AB=BC$.

Describe Euclid's $5^{\mathrm{th}}$ postulate.

Euclid's fifth postulate does imply the existence of parallel lines.

In the above figure, $\angle 3+\angle 4>180°$. If the lines $l$ and $m$ are produced indefinitely they will meet on that side on which $\angle 3+\angle 4>180°$.

In the adjacent figure,  a line$n$ falls on lines$l$ and $m$ such that the sum of the interior angle$\angle 1$ and $\angle 2$ is less than $180°$.On which side of the transversal $n$ will the line $l$ and line $m$ meet?

State Euclid's fifth postulate. Mention one significance of Euclid's fifth postulate.

A line which lies evenly with the points on itself is called a 

A straight line is a line which does not lies evenly with the points on itself.

Which of these following statement is true.

A straight line is a line which lies evenly with the _____ on itself.

State Euclid's definition of a straight line.

The ends of a line segment are points.

A _____ is that which has no part. 

In geometry a point, a line and a plane are undefined.

Why do we represent a point as a dot in the definition given by Euclid, even though it has some dimension.

The edges of the surface are

"A circle can be drawn with any centre and any radius" is Euclids