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Yogita Ingle 4 years, 1 month ago
A plane, in geometry, prolongs infinitely in two dimensions. It has no width. We can see an example of a plane in coordinate geometry. The coordinates define the position of points in a plane.
Posted by 𝑺𝒖𝒓𝒂𝒃𝒉𝒊 𝑺𝒂𝒖𝒎𝒚𝒂 4 years, 1 month ago
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Alok Gupta 4 years, 1 month ago
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Sia ? 3 years, 5 months ago
a formal examination of evidence by a judge, typically before a jury, in order to decide guilt in a case of criminal or civil proceedings.
Posted by Kamal Dhanusj 4 years, 1 month ago
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Yogita Ingle 4 years, 1 month ago
Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
Proof: Let p(x) be any polynomial with degree greater than or equal to 1. Suppose that when p(x) is divided by x – a, the quotient is q(x) and the remainder is r(x), i.e., p(x) = (x – a) q(x) + r(x) -- (i)
Since the degree of x – a is 1 and the degree of r(x) is less than the degree of x – a, the degree of r(x) = 0. This means that r(x) is a constant, say r. Thus we can re-write eq (i) as p(x) = (x – a) q(x) + r –(ii)
In particular, if x = a, then eq (ii) becomes p(a) = (a – a) q(a) + r = r,
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Yogita Ingle 4 years, 1 month ago
Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Proof:
Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.
Since PQ is a straight line, it can be concluded that:
∠PAB + ∠BAC + ∠QAC = 180° ………(1)
Since PQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
∠ACB + ∠BAC + ∠CBA= 180°
Thus, the sum of the interior angles of a triangle is 180°.
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A line a line which intersects two or more lines at distinct points is called a transversal.
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Sanjay Kumar 4 years, 1 month ago
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