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
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.
How many lines can be drawn through a given point.
In how many lines two distinct planes can intersect?
How many planes can be made to pass through three distinct points?
The number of dimension, a point has ______.
Euclid divided his famous treatise “The Elements” into ______.
In ancient India, the shapes of altars used for household rituals were ______.
Greek’s emphasised on ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
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.
