Advertisements
Advertisements
प्रश्न
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
Advertisements
उत्तर
Given, ∠ABC = ∠ACB ...(i)
And ∠4 = ∠3 ...(ii)
According to Eulid’s axiom, if equals are subtracted from equals, then remainders are also equal.
On subtracting equation (ii) from equation (i), we get
∠ABC – ∠4 = ∠ACB – ∠3
⇒ ∠1 = ∠2
Now, in ABDC, ∠1 = ∠2
⇒ DC = BD ...[Sides opposite to equal angles are equal]
BD = DC.
APPEARS IN
संबंधित प्रश्न
The following statement is true or false? Give reason for your answer.
Only one line can pass through a single point.
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.
In how many lines two distinct planes can intersect?
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 ______.
A pyramid is a solid figure, the base of which is ______.
Greek’s emphasised on ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
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.
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.
