Advertisements
Advertisements
Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
Advertisements
Solution
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
RELATED QUESTIONS
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
perpendicular lines
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.)
How many least number of distinct points determine a unique line?
In how many points a line, not in a plane, can intersect the plane?
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is ______.
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.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
