Advertisements
Advertisements
Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.

Advertisements
Solution
Given, ∠1 = ∠2 ...(i)
And ∠2 = ∠3 ...(ii)
According to Euclid’s axiom, things which are equal to the same thing are equal to one another.
From equations (i) and (ii),
∠1 = ∠3
APPEARS IN
RELATED QUESTIONS
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?
parallel lines
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.
If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
Given three distinct points in a plane, how many lines can be drawn by joining them?
Euclid belongs to the country ______.
Thales belongs to the country ______.
The things which are double of the same thing are equal to one another.
Read the following statements which are taken as axioms:
- If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
- If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
The following statement is true or false? Give reason for your answer.
There are an infinite number of lines which pass through two distinct points.
The following statement is true or false? Give reason for your answer.
A terminated line can be produced indefinitely on both the sides.
