Advertisements
Advertisements
Question
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
radius of a circle
Advertisements
Solution
Yes, we need to understand terms like point, line, ray, angle, plane, circle, and quadrilateral before defining the required terms.
The distance from the centre to a point on the circle is called the radius of the circle. In the figure, p is the centre, Q is a point on the circle, and PQ is the radius.
APPEARS IN
RELATED QUESTIONS
Consider two ‘postulates’ given below:-
- Given any two distinct points A and B, there exists a third point C which is in between A and B.
- 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.
In how many points two distinct lines can intersect?
In how many points a line, not in a plane, can intersect the plane?
The things which are double of the same thing are equal to one another.
If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
Solve the following question using appropriate Euclid’s axiom:
Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.
In the following figure AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.
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.
