Advertisements
Advertisements
Question
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
Solution
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
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
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.)
Given three distinct points in a plane, how many lines can be drawn by joining them?
The number of dimension, a point has ______.
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
In ancient India, the shapes of altars used for household rituals were ______.
The edges of a surface are curves.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.
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.
