Advertisements
Advertisements
Question
In the following figure, if AC = BD, then prove that AB = CD.
Advertisements
Solution
From the figure, it can be observed that
AC = AB + BC
BD = BC + CD
It is given that AC = BD
AB + BC = BC + CD ...(1)
According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal.
Subtracting BC from equation (1), we obtain
AB + BC − BC = BC + CD − BC
AB = CD
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?
radius of a circle
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.
Given three distinct points in a plane, how many lines can be drawn by joining them?
The side faces of a pyramid are ______.
In ancient India, the shapes of altars used for household rituals were ______.
Thales belongs to the country ______.
The statements that are proved are called axioms.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
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 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.
