The document RD Sharma Solutions - Chapter 15 - Understanding Shapes-I (Polygons), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**PAGE NO 15.5:**

**Question 1:**

**Draw rough diagrams to illustrate the following: (i) Open curve (ii) Closed curve**

**ANSWER:**

(i) Open curve: A curve in which the beginning and the end points does not cut each other or are different.

(ii) Closed curve: A curve in which the beginning and the end points are the same and cuts each other.

**Question 2:**

**Classify the following curves as open or closed:**

**ANSWER:**

Open curve: A curve in which the beginning and end points are different or do not cut each other.

Closed curve: A curve in which the beginning and end points are the same and cut each other.

By the above definitions, we can classify the given figures as follows:

(i) Open curve

(ii) Closed curve

(iii) Closed curve

(iv) Open curve

(v) Open curve

(vi) Closed curve

**Question 3:**

**Draw a polygon and shade its interior. Also draw its diagonals, if any.**

**ANSWER:**

In polygon ABCD, AC and BD are the diagonals.

**PAGE NO 15.6:**

**Question 4:**

**Illustrate, if possible, each one of the following with a rough diagram: (i) A closed curve that is not a polygon. (ii) An open curve made up entirely of line segments. (iii) A polygon with two sides.**

**ANSWER:**

(i) Polygons are made up of straight lines, not curves.

(ii) An open curve made up entirely of line segments:

(iii) Not possible because polygons are closed figures.

**Question 5:**

**Following are some figures: Classify each of these fugures on the basis of the following: (i) Simple curve (ii) Simple closed curve (iii) Polygon (iv) Convex polygon (v) Concave polygon (vi) Not a curve**

**ANSWER:**

(i) It is a simple closed curve and a concave polygon.

(ii) It is a simple closed curve and a convex polygon.

(iii) It is not a curve; hence, it is not a polygon.

(iv) It is not a curve; hence, it is not a polygon.

(v) It is a simple closed curve but not a polygon.

(vi) It is a simple closed curve but not a polygon.

(vii) It is a simple closed curve but not a polygon.

(viii) It is a simple closed curve but not a polygon.

**Question 6:**

**How many diagonals does each of the following have? (i) A convex quadrilateral (ii) A regular hexagon (iii) A triangle**

**ANSWER:**

An n-sided convex polygon has diagonals.

(i) A quadrilateral has diagonals.

There are 2 diagonals in the convex quadrilateral.

(ii) A regular hexagon has diagonals.

There are 9 diagonals in a regular hexagon.

(iii) A triangle does not have any diagonal in it.

**Question 7:**

**What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides**

**ANSWER:**

A polygon that has equal sides and equal angles is called a regular polygon.**(i) Equilateral triangle:****(ii) Square:****(iii) Regular hexagon:**

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