Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given, X is the mid-point of AC
AX = CX = `1/2` AC
⇒ 2AX = 2CX = AC ...(i)
And Y is the mid-point of BC.
BY = CY = `1/2` BC
⇒ 2BY = 2CY = BC ...(ii)
Also, given AX = CY ...(iii)
According to Euclid’s axiom, things which are double of the same things are equal to one another.
From equation (iii), 2AX = 2CY
⇒ AC = BC ...[From equation (i) and (ii)]
APPEARS IN
RELATED QUESTIONS
In the following figure, if AC = BD, then prove that AB = CD.
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.)
The three steps from solids to points are ______.
Euclid divided his famous treatise “The Elements” into ______.
The total number of propositions in the Elements are ______.
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio ______.
Euclid belongs to the country ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
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.
