RS Aggarwal Class 9 Solutions Chapter 3 Introduction to Euclid’s Geometry Ex 3A
These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 3 Introduction to Euclid’s Geometry Ex 3A.
What is the difference between a theorem and an axiom.
A theorem is a statement that requires a proof while an axiom is the basic fact which is taken for granted without proof.
Define the following terms :
(i) Line segment
(iii) Intersecting lines
(iv) Parallel lines
(vi) Concurrent lines
(vii) Collinear points
(i) Line segment: The straight line between two points A and B is a called a line segment
(ii) Ray : A line segment when extended indefinitely is one direction is called a ray It has no definitely length.
(iii) Intersecting lines : Two lines having one common point are called intersecting lines and the common point is called the point of intersection.
(iv) Parallel Lines : If two lines lying in the same plane do not intersect each other when produced on either side, then these two lines are called parallel lines. The distance between two parallel hues always remains the same.
(v) Half line : If we take a point P on a line , its divides the line into two parts. Each part is called half line or two ray i.e. and .
(vi) Concurrent lines : Three or more lines intersecting at the same point are called concurrent lines.
(vii) Collinear points : Three or more points lying on the same line are called collinear points.
(viii) Plane : A plane is a surface such that every point of the line joining any two points on it, lies on it.
In the adjoining figure, name :
(i) Six points
(ii) Five line segments
(iii) Four rays
(iv) Four lines
(v) Four collinear points
(i) Six points are : A, B, C, D, E and F
(ii) Five line segments are : , , , and
(iii) Four rays are : , , and
(iv) Four lines are : ,, and
(v) Four collinear points are M, E, G, B. Ans
In the adjoining figure, name :
(i) Two pairs of intersecting lines and their corresponding points of intersection
(ii) Three concurrent lines and their points of intersection
(iii) Three rays
(iv) Two line segments
(i) and is a pair of intersecting line whose point of intersection is R
and second pair of intersecting lines is and and point of intersection is P.
(ii) Three concurrent lines are , and and the point of intersection is R.
(iii) Three rays are , and
(iv) Two line segments are and
(i) How many lines can be drawn to pass through a given point ?
(ii) How many lines can be drawn to pass through two given points ?
(iii) In how many points can the two lines at the most intersect ?
(iv) If A, B, C are three collinear points, name all the line segments determined by them.
(i) Through a given point, infinitely many lines can be drawn.
(ii) Only one line can be drawn to pass through two given points.
(iii) Two lines can intersect each other at the most one point
(iv) A, B and C are three collinear points. Then the line segments will be , and .
Which of the following statements are true ?
(i) A line segment has no definite length.
(ii) A ray has no end point.
(iii) A ray has a definite length.
(iv) A line is the same as line .
(v) A line is the same as ray
(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two distinct lines cannot have more than one point in common.
(ix) Two intersecting lines cannot be both parallel to the same line.
(x) Open half-line OA is the same thing as ray
(xi) Two lines may intersect in two points.
(xii) Two lines l and m are parallel only when they have no point in common.
(iv), (vi), (vii), (viii) and (ix) are true and others are not true.
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