Advertisements
Advertisements
Question
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
Solution
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
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?
line segment
How many planes can be made to pass through a line and a point not on the line?
The number of dimensions, a solid has ______.
Boundaries of surfaces are ______.
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is ______.
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom.
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?
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have BX = `1/2` AB, BY = `1/2` BC and AB = BC. Show that BX = BY.
Read the following two statements which are taken as axioms:
- If two lines intersect each other, then the vertically opposite angles are not equal.
- If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.
Is this system of axioms consistent? Justify your answer.
Read the following axioms:
- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.
