Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, AB = BC ...(i)
M is the mid-point of AB.
∴ AM = MB = `1/2` AB ...(ii)
And N is the mid-point of BC.
∴ BN = NC = `1/2` BC ...(iii)
According to Euclid’s axiom, things which are halves of the same things are equal to one another.
From equation (i), AB = BC
On multiplying both sides by `1/2`, we get
`1/2` AB = `1/2` BC
⇒ AM = NC ...[Using equations (ii) and (iii)]
APPEARS IN
संबंधित प्रश्न
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.
In how many lines two distinct planes can intersect?
How many least number of distinct points determine a unique plane?
How many planes can be made to pass through three distinct points?
Thales belongs to the country ______.
The boundaries of the solids are curves.
The things which are double of the same thing are equal to one another.
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.
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
