Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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.
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
How many lines can be drawn through both of the given points?
How many lines can be drawn through a given point.
In how many points a line, not in a plane, can intersect the plane?
Euclid divided his famous treatise “The Elements” into ______.
The boundaries of the solids are curves.
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.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
The following statement is true or false? Give reason for your answer.
A terminated line can be produced indefinitely on both the sides.
