Q. 35.0( 3 Votes )

Read the following statements which are taken as axioms:

(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.

(ii) If a transversal intersects two parallel lines, then alternate interior angles are equal.

Is this system of axioms consistent? Justify your answer.

Answer :

A system of axiom is called consistent, if there is no statement which can be deduced from these axioms such that it contradicts any axioms.

We know that, if a transversal intersects two parallel line, then each pair of corresponding angles are equal, which is a theorem. So, statement (i) is false and not an axiom.


Also, we know that, if a transversal intersects two parallel line, then each pair of alternate interior angles are equal. It is also a theorem. So, statement(ii) is true and an axiom.


Thus, in given statements, first is false and second is an axiom.


Hence, given of axioms is not consistent.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Know About Euclids GeometryKnow About Euclids GeometryKnow About Euclids Geometry46 mins
Euclid's Fifth Postulate and its ApplicationsEuclid's Fifth Postulate and its ApplicationsEuclid's Fifth Postulate and its Applications36 mins
Euclid's GeometryEuclid's GeometryEuclid's Geometry51 mins
Euclid's Most Interesting Postulate.Euclid's Most Interesting Postulate.Euclid's Most Interesting Postulate.42 mins
Doubt Session  - Introduction to Euclid's GeometryDoubt Session  - Introduction to Euclid's GeometryDoubt Session - Introduction to Euclid's Geometry32 mins
Quiz | Imp. Qs. on Coordinate GeometryQuiz | Imp. Qs. on Coordinate GeometryQuiz | Imp. Qs. on Coordinate Geometry39 mins
Know How to Solve Complex Geometry Problems!Know How to Solve Complex Geometry Problems!Know How to Solve Complex Geometry Problems!27 mins
Introduction to HeatIntroduction to HeatIntroduction to Heat45 mins
Coordinate GeometryCoordinate GeometryCoordinate Geometry45 mins
Quiz | Euclid's GeometryQuiz | Euclid's GeometryQuiz | Euclid's Geometry44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :