Advertisements
Advertisements
प्रश्न
In the following figure, if AC = BD, then prove that AB = CD.
Advertisements
उत्तर
From the figure, it can be observed that
AC = AB + BC
BD = BC + CD
It is given that AC = BD
AB + BC = BC + CD ...(1)
According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal.
Subtracting BC from equation (1), we obtain
AB + BC − BC = BC + CD − BC
AB = CD
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.
How many lines can be drawn through both of the given points?
Given three distinct points in a plane, how many lines can be drawn by joining them?
The number of dimensions, a solid has ______.
Euclid divided his famous treatise “The Elements” into ______.
Boundaries of surfaces are ______.
Pythagoras was a student of ______.
Solve the following question using appropriate Euclid’s axiom:
Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
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.
