Advertisements
Advertisements
Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.
Advertisements
Solution
Given OX = `1/2` XY
⇒ 2OX = XY ...(i)
PX = `1/2` XZ
⇒ 2PX = XZ ...(ii)
And OX = PX ...(iii)
According to Euclid’s axiom, things which are double of the same things are equal to one another.
On multiplying equation (iii) by 2, we get
2OX = 2PX
XY = XZ ...[From equations (i) and (ii)]
APPEARS IN
RELATED QUESTIONS
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.
Given three distinct points in a plane, how many lines can be drawn by joining them?
The three steps from solids to points are ______.
The total number of propositions in the Elements are ______.
Boundaries of solids are ______.
Pythagoras was a student of ______.
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:
Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.
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 ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
