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
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?
parallel lines
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
In ancient India, the shapes of altars used for household rituals were ______.
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for ______.
Thales belongs to the country ______.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AB = BC, BX = BY. Show that AX = CY.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3.
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.
The following statement is true or false? Give reason for your answer.
There are an infinite number of lines which pass through two distinct points.
