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.
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
In how many lines two distinct planes can intersect?
How many planes can be made to pass through two points?
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
The statements that are proved are called axioms.
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:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
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.
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.
Read the following statements which are taken as axioms:
- If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
- If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
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.
