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?
perpendicular lines
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?
line segment
How many least number of distinct points determine a unique line?
How many planes can be made to pass through two points?
The number of dimensions, a surface has ______.
Boundaries of solids are ______.
The side faces of a pyramid are ______.
In ancient India, the shapes of altars used for household rituals were ______.
Thales belongs to the country ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.
