Question

19. Quadratic equation has two 1 point
real roots when --
D>0
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D>=0
D<0​

Answer 1

Answer:

27. Opposite Rays: Two rays AB and AC are said to be opposite rays if they are collinear and point A is the only common point of these two rays.

other so as to cover it completely and exactly.

20. Line Segment Length Axiom: Every line segment has a length. It is measured in terms of ‘metre’ or Its parts.

21. Congruent Line Segment Length Axiom: Two congruent line segments have equal length and conversely, two line segments of equal length are congruent,

i.e., AB ≌ CD ⇔ l (AB) = l (CD).

22. Line Segment Addition Axiom: If C is any interior point of a line segment AB, then

23. Line Segment Construction Axiom: Given a point O on a line l and a positive real number r, there are exactly two points P1 and P2 on l, on either side of O such that

l (OP1) = l (OP2) = r cm.

24. Distance between Two Points: The distance between two points P and Q is the length of the line segment joining them and it is denoted by PQ.

25. Betweenness: Point C is said to lie between the two points A and B, if

(a) A, B and C are collinear points and

(n) AC + CB = AB.

26. Mid-point of a Line Segment: Given a line segment AB, a point M is said to be the mid-point of AB, if M is an interior point of AB such that AM = MB.

Line through M, other than line AB is called the bisector of the segment AB.

27. Opposite Rays: Two rays AB and AC are said to be opposite rays if they are collinear and point A is the only common point of these two rays.

Note: Two rays or two line segments or a line segment and a ray (line) are said to be parallel, if the lines containing them are parallel.

28. Euclid’s Five Postulates:

(a) A straight line may be drawn from any one point to any other point.

(b) A terminated line can be produced indefinitely.

(c) A circle can be drawn with any centre and any radius.

(d) All right angles are equal to one another.

(e) If a straight line falling on two straight lines makes the interior angles on the same side of it, taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

29. Some Euclid’s axioms:

(a) Things which are equal to the same thing are equal to one another.

(b) If equals are added to equals, the wholes are equal.

(c) If equals are subtracted from equals, the remainders are equal.

(d) Things which coincide with one another are equal to one another.

(e) The whole is greater than the part.

(f) Things which are double of the same things are equal to one another.

(g) Things which are halves of the same things are equal to one another.

30. A system of axioms is called consistent, if it is impossible to deduce from these axioms a statement that contradicts any axioms or previously proved statement.