Maths M.C.Q

A solid has shape, size, position and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from the other.

An axiom is a proposition regarded as self-evidently true without proof​​​​​​.

A point has no length and no breadth.
A point is that which has no part.

A ray starts at a given point and goes off in a certain direction to infinity. The point where the ray starts is called the endpoint.

The Euclid’s axiom that illustrates the given statement is second axiom, according to which. If equals are added to equals, the wholes are equal.

One

Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.

The side faces of a pyramid are triangles.

If two line segments are equal then they are called congruent segments.

A terminated line can be produced indefinitely on both sides.

A pyramid is a solid figure, whose base is any polygon.

A rectilinear figure is a figure all of whose edges meet at right angles.
A circle has no edge.

Same

A straight line may be drawn from any point to any other point.

Euclid's fifth postulate can also be stated in the following form: Two distinct intersecting lines cannot be parallel to the same line.

Lines

Infinite number of lines can pass through a single point.

Length and breadth only

The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning. A Greek mathematician, Thales is credited with giving the first known proof.

If equals be subtracted from equals, the remainder are equal.

Equal

Only one line can pass through two given distinct points.

Squares and circular altars were used for household rituals.
Whereas altars having shapes as combinatiotanglens of recs, triangles and trapeziums were used for public worship.

The boundaries of surfaces are curves.

When three or more lines intersect in one point, they are concurrent.
The point at which they intersect is the point of concurrency.

According to Euclid's 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.

Thales belongs to the country Greece.
The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning.
Thales, a Greeks mathematician, is credited with giving the first known proof.

When two lines are parallel to the same line, they are parallel to each other.

Thales

A statement that requires a proof is called a theorem.

Because point has no part.

If equals be added to equal, the whole are equal.

A line segment is a piece, or part, of a line in geometry.
A line segment is represented by endpoints on each end of the line segment.
A line in geometry is represented by a line with arrows at each end.
A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end.

Either intersect or parallel

Radius

Axioms are assumed universal truths in all branches of mathematics and no mathematical deduction is needed to prove them.

A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.

Boundaries of solids are surfaces.

In ancient India, squares and circular altars were used for household rituals.

A ray is part of a line, has one fixed endpoint, and extends infinitely along the line from the endpoint.

Euclid first postulates is:
A straight line may be drawn from any point to any other point

Clearly, it is a true statement as if we consider any two equal circles, then their radii are equal.

Axioms are assumed as universal truths in all branches of mathematics because they are taken for granted, without proof.

The edges of a surface are lines.

The side faces of a pyramid are always triangles.

Assumptions

Axioms

Boundaries of surfaces are curves.

Infinite number of lines can pass through a single point.

Things which are halves of the same things are equal to each other.

Innumerable

A pyramid is a polyhedron formed by connecting of polygonal base and an apex.
Each base edge and apex forms a triangle, called the lateral face.
It is a conic solid with polygonal base.

Surfaces

A line has no endpoint. It extends in both the directions endlessly.

In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship.

According to Euclid's fifth postulate, if a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.

Edge is a line or border at which a surface terminates.

Lines

Euclid belongs to the country, Greece.

When the side faces of a polyhedron are rectangles then it is known as prism.

From ancient times, axioms have been acquired by man through the day to day experiences.
No mathematical deduction is needed to prove them.
So axioms are assumed universal truths in all branches of mathematics.

Because when we connect base edge and apex it forms a triangle.

The Euclid’s axiom that illustrates the given statement is second axiom, according to which. If equals are added to equals, the wholes are equal.

The whole is made up of its parts, hence, it will always be greater than the part.

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.

The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is nine.

A line segment has two end points.

Clearly floor and the ceiling of a room are opposite to each other and do not intersect at any point, hence are parallel planes.

Any polygon

A point has 0 dimensions.

A solid shape also has a depth. solids by their nature have an inside and an outside separated by a surface. that's why solid is a three-dimensional struture. It has length, breadth, and depth.

If equals are added to equals, the whole are equals.

Because solid has both inner and outer part separated by surface.

According to Euclid's common notions, the whole is greater than the part.

Surfaces

A postulate

Euclid's fourth postulate states that all right angles are equal to one another.

A solid has shape, size, position and can be moved from one place to another. So, a solid has three dimensions.
For example: cuboid, cube, cylinder, cone etc.

Because surface has both length and breadth which are lines.

Five

The statements that were proved are called propositions or theorems.

Both Assertion and reason are correct and reason is correct explanation for Assertion.

(B) 

Radius

Lines which are concurrent have only one point in common and is called the point of concurrency.

Thales belongs to the country, Greece.

Euclid stated that all right angles are equal to each other in the form of a postulate.

Since the three points are collinear, they lie on the same line, so only one line can be determined by them.

A postulate

If two line segments are equal then they are called congruent segments.

Second axiom states that if equals be added to equals, then wholes are equal.

Equal

Any polygon

Three

According to Euclid's first axiom that thing which is equal to the same thing, are equal to one another.
Hence, If two lines are equal to a third line, they will be equal in length.

Because a line is a breathless length.

Boundaries of solids are called surfaces.

The Sriyantra consists of nine interwoven isosceles triangles.

In ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for public rituals.

Squares and circles

Only a square

A sentence which is either true or false but not both is called the statement.

The radius of a circle is the distance from the center of the circle to any point on its circumference.

Things which are double of the same things are equal to each other.

Lines are parallel if they do not intersect' is started in the form of a definition.

In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship.

The whole is lesser than the part.

The whole is greater than the part.

Surfaces

If the points are collinear then only one line can pass through them as collinear means "on the same line".

Lines