Advertisements
Advertisements
प्रश्न
In the following figure BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
Advertisements
उत्तर
Given, BM = BN ...(i)
M is the mid-point of AB.
∴ AM = BM = `1/2` AB
⇒ 2AM = 2BM = AB ...(ii)
And N is the mid-point of BC.
∴ BN = NC = `1/2` BC
⇒ 2BN = 2NC = BC ...(iii)
According to Euclid’s axiom, things which are double of the same thing are equal to one another.
On multiplying both sides of equation (i) by 2, we get
2BM = 2BN
⇒ AB = BC ...[Using equations (ii) and (iii)]
APPEARS IN
संबंधित प्रश्न
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
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
How many lines can be drawn through both of the given points?
How many planes can be made to pass through two points?
The three steps from solids to points are ______.
Euclid divided his famous treatise “The Elements” into ______.
Boundaries of surfaces are ______.
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
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.
Solve the following question using appropriate Euclid’s axiom:
It is known that x + y = 10 and that x = z. Show that z + y = 10?
