## NCERT 6TH CLASS MATHEMATICS CHAPTER BASIC GEOMETRICAL IDEAS

**POINT**

A point shows an exact location of an object. It is the basic unit of geometry. It is represented with the help of a dot. It is named by using a single capital English alphabet.

** LINE, LINE SEGEMENT, AND RAY**

**(a) Intersecting Lines :**

**(b) Parallel Lines :**

**(c) Line segment **:

**(d) Ray :**

**(e) Collinear Points:**

**NOTE :**

**(f) Concurrent lines**

**NOTE **:

**Curves**

**Open and Closed figures**

**Open figure :**The figures that do not begin and end at the same point are called open figures.

**Closed figure :**The figures that begin and end at the same point are called closed figures. They are also called closed curves. The closed curves that do not cross themselves are called simple closed curve. For example : triangle, circle, ellipse, rectangle, square, etc. are all closed figures.

**POLYGON**

**lnterior and exterior of closed figures :**

**ANGLE**

**lnterior of an angle :**

**Exterior of an angle : **

**Adjacent Angles :**

**TRIANGLE**

**Medians of a Triangle :**

**Altitudes of a Triangle :**

**QUADRILATERAL**

**Elements of a Quadrilateral :**

**Adjacent sides :**In the quadrilaterial PQRS there are four sides, namely , , and .

**Opposite sides :**The sides and are called opposite sides. Similarly, and are also opposite sides. They have no common end point.

**Adjacent angles :**Two angles of a quadrilateral which have a common arm are called adjacent angles.

**Opposite angles :**ÐP and ÐR are opposite angles as they have no common arm.

**lnterior and exterior of a quadrilaterial :**

**CRICLE**

**Parts of a Circle**

**chord**of that circle.

**diameter**of that circle.

**NOTE : **

**circumference.**

**A Few More Definitions**

**1. Secant.**A line which intersects or meets the circle at two distinct points is called a secant.

**2. Arc.**A part (continuous) of a circle is called an arc.

**3. Semi-circle.**A diameter divides a circle into two equal parts which are called semi-circles.

**4. Segment.**A chord AB of a circle divides the area enclosed by it into two parts which are called segments.

**5. Sector and Quadrant.**The part of a circle enclosed by any two radii of the circle is called a sector of the circle.

**6. Concentric Circles :**Two or more circles drawn with the same centre are called concentric circles.

**OBJECTIVE TYPE**

Q.1 Which of the following figures is made of line segments only?

(A) (B) (C) (D)

Q.2 Which of the following is another name for ÐABC?

(A) ÐA (B) ÐCBA (C) ÐACB (D) ÐCAB

Q.3 Which of the following rays are the arms of ÐBOA?

(A) OB, OE (B) OE, OA (C) OB, OA (D) OC, OA

Q.4 Which of the following is not a pair of adjacent angles of quadrilateral ABCD ?

(A) ÐA, ÐB (B) ÐC, ÐD (C) ÐB, ÐD (D) ÐD, ÐA

Q.5 A quadrilateral has

(A) 2 diagonals, 3 angles (B) 4 diagonals, 4 angles

(C) 2 diagonals, 4 angles (D) 4 diagonals, 4 sides

Q.6 The complete distance around a circle is called the

(A) Secter (B) Quadrant (C) Circumference (D) Segment

Q.7 One-fourth part of a circle is known as a

(A) semi-circle (B) major segment (C) sector (D) quadrant

Q.8 The longest chord of a circle is known as a

(A) radius (B) diameter (C) circumference (D) secant

Q.9 An arc is a continuous part of the _______ of the circle.

(A) diameter (B) major segment (C) circumference (D) chord

Q.10 The centre of the circle always lies in the interior of the

(A) minor segment (B) semi-circle (C) major segment (D) plane

Q.11 An exact location in space is called a

(A) ray (B) point (C) line segment (D) plane

Q.12 Which of the following has no end points ?

(A) (B) (C) (D)

Q.13 a quadrilateral is a simple closed figure formed by ________ line segments.

(A) 3 (B) 4 (C) 2 (D) 5

Q.14 The radius of a circle is 3 cm. Its diameter is

(A) 1.5 cm (B) 9 cm (C) 4.5 cm (D) 6 cm

Q.15 The end points of a diameter of a circle divide the circle into two parts, each of which is known as

(A) segment (B) sector (C) semi-circle (D) quadrant

Q.16 What is three or more lines called if they pass through a common point ?

(A) parallel lines (B) intersecting lines (C) concurrent (D) none of these

Q.17 How many end points does a ray has ?

(A) one (B) two (C) three (D) zero

Q.18 Two angles of a quadrilateral having a common side are called :

(A) opposite angles (B) equal angles (C) adjacent angles (D) none of these

Q.19 The point where a pair of adjacent sides of a polygon meets is called :

(A) diagonal (B) adjacent angles (C) vertex (D) none of these

Q.20 Diameter =

(A) 2 × radius (B) 2 (C) radius (D) 1/2 × radius

**SUBJECTIVE TYPE**

Q.1 Write :

(i) All pairs of parallel lines.

(ii) All pairs of intersecting lines.

(iii) Lines whose points of intersection is L.

Q.2

Name the six angles in the diagram above that have C as a vertex.

Q.3 In Fig. name the lines which are concurrent at the point

(i) A (ii) O (iii) B

Name also the sets of collinear points.

Q.4 In the given triangle, S is mid point of QR :

(i) The side opposite to vertex P, in DPQR.

(ii) The altitude from vertex P, in DPQR.

(iii) The angle opposite to side PQ, in DPQT.

(iv) The vertex opposite to side PR in DPQR.

(v) The median from vertex P, in DPQR.

Q.5 Two points A and B are given. How many circles can be drawn

(i) passing through both the points ?

(ii) with A as centre and AB as radius ?

Q.6 O is the centre of the two circles in the figure drawn below. Fill up the blanks in the following :

(i) _______ are radii of the inner circle.

(ii) OA, OQ, OP are the ________ of the ________ circle.

(iii) LM is a ________ of the ________ circle.

(iv) PQ is a ________ of the ________ circle.

(v) The two circles are called ________ circles.

(vi) LXM is a ________ of the ________ circle.

(vii) POA is a _________ of the _________ circle.

Q.7 Answer True (T) or False (F) :

(i) Only one ray can be drawn with a given initial point.

(ii) Two planes intersect in a line.

(iii) The interior of a triangle, and the triangle itself make the triangular region.

(iv) In a quadrilateral PQRS, P and R are a pair of adjacent angles.

(v) The line segments joining the centre of the circle and any point on the circle are all equal.

(vi) A segement is a figure enclosed by a chord and the corresponding arc of the circle.

(vii) The distance of a point which is in the interior of a circle from the centre, is less than its radius.

(viii) Two concentric circle have two distinct centres.

Q.8 Name the doted/shaded part.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Q.9 In a quadrilateral, define each of the following :

(i) Sides (ii) Vertices (iii) Angle

(iv) Diagonals (v) Adjacent sides (vi) Adjacent angles

(vii) Opposite angles (viii) Opposite sides

Q.10 Classify the following as open or closed :

(i)

(ii)

(iii)

(iv)

(v)