Chapter-4 Basic Geometrical Ideas - Worksheet

Explanation:

(a) From the above figure, we have to name five points. So by seeing the figure we can say that five points are D, E, O, B and C.

(b) From the above figure, we have to name a line. A line is a connection between the two points, and the line moves in both the directions. So, in the above figure line is 

(c) From the above figure, we have to name a rays. A ray is the line emerging from a point and moves in only one direction. So, in the above figure there are total four rays, , , and .

(d) From the above figure, we have to name five line segments. A line segments is line joining two points and doesn’t continues in any direction. So, the five line segments are , , , and 

Explanation:

From the above figure, we have to name all possible line. A line is a connection between the two points, and the line moves in both the directions. So, the all possible lines are , , , , , , , , , , , 

Explanation:

(a) Here, from the above figure, we can say that the line   is passing through point E and contains point E.

(b) Here, from the above figure, we can say that the line  if paying through the point A.

(c) Here, from the above figure, we can say that the line the point O lies.

(d) Here, from the above figure, we can say that  , and ,  are the two intersecting pair of lines.

Explanation:

(a) From the definition of line, a line is a connection between the two points. Now, if there is only one point than infinite lines can be pass through that point. 

(b) From the definition of line, a line is a connection between the two points. Now, if we fix that the is only two points, then only one line is possible.

Explanation:

(a)

Here, it is given that point P lies on the line AB.

(b)

Here, it is given that line XY and line PQ are intersection at point M.

(c)

Here, it is given that line l contains the point E and F but not D.

(d)

Here, it is given that line OP and OQ mere at O. Now, in both the line one point is save that is point O. So, the lines will meet at point O.

Explanation:

1. True

Here, from the above figure we can say that points Q,M,O,N and P lies on line MN.

2. True

Here, from the above figure we can say that point M,O and N are the points in line segment MN.

3. True

Here, from the above figure we can say that point M and N are the end points of the line segment MN.

4. False

Here, from the above figure we can say that point O and N are not the end one of line segment OP.

5. False

Here, from the above figure we can say that point M is not  the end points of line segment QO.  

6. False

Here, from the above figure we can say that point M is not on the line OP.

7. True

Here, from the above figure we can say that line OP is different from line QP.

8. False

Here, from the above figure we can say that ray OP and ray OM are different.

9. False

Here, from the above figure we can say that OM is opposite to OP. 

10. False

Here, from the above figure we can say that point O is the initial point of line OP.

11. True

Here, from the above figure we can say that point N is the initial point for the line NP and line NM.

Explanation:

1. when the starting and end points are same than the curve is know as closed curve but if the starting and end points are not same than the curve is known as open curve.

Here, we have given an open curve

2. when the starting and end points are same than         the curve is know as closed curve but if the starting and end points are not same than the curve is known as open curve.

Here, we have given a closed curve.

3. when the starting and end points are same than the curve is know as closed curve but if the starting and end points are not same than the curve is known as open curve.

Here, we have given an open curve.

4. when the starting and end points are same than the curve is know as closed curve but if the starting and end points are not same than the curve is known as open curve.

Here, we have given a closed curve.

5. when the starting and end points are same than the curve is know as closed curve but if the starting and end points are not same than the curve is known as open curve.

Here, we have given a closed curve.

Explanation:

(a) When the starting and end points are not same than the curve is known as open curve. The below figure is an open curve.

(b) When the starting and end points are same than the curve is know as closed curve. The below figure is a closed curve.

Explanation:

When any shape of drawn with more than four sides are known as polygon. Polygon is a closed figure. So, the number of point will remain same as the number of sides. The below figure is a polygon with a shaded interior.

Explanation:

(a) Yes, the above given shape is a curve

(b) Yes, the above given shape is a closed curve. When the starting and end points are same than the curve is know as closed curve.

Explanation:

(a)When any shape of drawn with more than four sides are known as polygon. So, the only option we have to dream a circular figure which doesn’t have any side but forms a closed figure.

(b) When the starting and end points are not same than the curve is known as open curve. The below figure is an open curve. The below figure is an open curve made up entirely of line segments.

(c) When any shape of drawn with more than four sides are known as polygon. So, if the sides are only two than it will become a triangle.

Explanation:

Here, in the above given figure there are total four angle. The angles are ∠DAB, ∠ABC, ∠BCD and ∠CDA

Explanation:

(a) Here, from the above figure we can say that the point A is the interior point of ∠DOE.

(b) Here, from the above figure we can say that the points C,A and D are the exterior of ∠EOF.

(c) Here, from the above figure we can say that the points E,B,O and F are on ∠EOF.

Explanation:

(a) Here, from the above given condition we can draw the figure as O is the common point between ∠COD and ∠AOB

(b) Here, from the above given condition we can draw the figure as O and B are common points between ∠AOB and ∠BOC

(c) Here, from the above given condition we can draw the figure as O, E and B are common points between ∠AOB and ∠BOC

(d) Here, from the above given condition we can draw the figure as O, E, D and A are common points between ∠BOA and ∠COA

(e) Here, from the above given condition we can draw the figure as OC is a common ray between ∠BOC and ∠AOC

Explanation:

Here, from the above given condition we can draw the triangle ABC and mark the points P and Q. Now, point A lies on the triangle ABC. So, It lies neither in the interior nor the exterior.

Explanation:

(a)Here, from the above given figure we can say that ∠ABD, ∠ACB, ∠ADC are the three triangles.

(b) Here, from the above given figure we can say that ∠BAC, ∠BAD, ∠CAD, ∠ADB, ∠ADC, ∠ABC, ∠ACB are the seven angles.

(c) Here, from the above given figure we can say , , , , ,  are six line segments.

(d) Here, from the above figure we can say that ∠ABD and ∠ABC are triangles which have ∠B as common.

Explanation:

Here, from the above given condition we can draw the figure. Now,  PR and QS are the diagonals and they meet at point O. Grin the figure we can say that point O is the interior point of the quadrilateral.

Explanation:

(a) Here, from the above given condition we can draw the figure. Now, the pairs of opposite sides are
, and , 

(b) Here, from the above figure we can say that ∠KLM, ∠KNM and ∠LKN, ∠LMN are two pairs of opposite angles.

(c) Here, from the above figure we can say that
, and , or , and ,  are the two pairs of adjacent sides.

(d) Here, from the above figure we can say that ∠K, ∠L and ∠M, ∠N or ∠K, ∠L and ∠L, ∠M are the two pairs of adjacent angles.

Explanation:

(a) Here, from the above given figure we can say that O is the center of the circle.

(b) Here, from the above given figure we can say that  , ,  are three radii of the circle. 

(c) Here, from the above given figure we can say that is the diameter of the circle.

(d) Here, from the above given figure we can say that   is the chord of the circle.

(e) Here, from the above given figure we can say that O and P are the two points in the interior 

(f) Here, from the above given figure we can say that Q is the point on the exterior of the circle.

(g) Here, from the above given figure we can say that AOB is a sector of the circle.

(h) Here, from the above given figure we can say that ED is a segment of the circle.

Explanation:

(a) Yes, a straight line inside the circle is known as chord. Diameter is also a straight line inside the circle. So, every diameter of a circle is also a chord and the diameter is also called the longest chord.

(b) No, a straight line inside the circle is known as chord. But every straight line is not diameter. So, every chord is not a diameter.

Explanation:

(a) Here, from the above given condition we can draw the figure. Now, the center of the circle is O.

(b) Here, from the above figure we can say that OC is the radius of the circle.

(c) Here, from the above figure we can say that   is the diameter of the circle.

(d) Here, getting the above figure we can say that AOC is a sector of the circle.

(e) Here, from the above figure we can say that DE is a segment of the circle.

(f) Here, from the above figure we can say that point O is the interior point of the circle 

(g) Here, from the above figure we can say that the point F is the exterior point of the circle.

(h) Here, from the above figure we can say that is an arch of the circle.

Explanation:

(a) True, diameter is the longest chord which passes through the center. So, any diameter will pass through the center. So, two diameters will always intersect each other at the center of the circle.

(b) True, the center of the circle is the point from where the circle is drawn. So the center of the circle will always be in its interior.