# POLYGONS AND PLANE FIGURES

**Subject** : **Mathematics**

**Mathematics**

**Class** : Basic 6 / Primary 6 /Grade 6

**Term** : Third Term / 3rd Term

**Week** : Week 4

**Topic** : POLYGONS AND PLANE FIGURES

**Behavioural Objectives :** At the end of the lesson, the pupils should be able to

**Explain the meaning of polygons**- Give examples of polygons
- Mention types of polygons
- Say the properties of polygons

**Previous Knowledge : Pupils have previous knowledge of TYPES OF ANGLES that was taught in the previous lesson**

**Instructional Materials** :

- Pictures
- Wall Posters
- Related Online Videos
- Role Playing

**Reference Materials**

- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- 9 Year Basic Education Curriculum

**Content** :

**POLYGON AND PLANE FIGURES**

**A polygon is a shape with straight sides. Polygons are shapes . Shapes are the appearance or look of things There are regular polygons and irregular polygons . Squares , rectangles , Triangles and quadrilaterals are polygons. Some**

**other polygons have special names.**

**Number of straight lines or sides in polygons **

**3 Triangle**

**4 Quadrilateral**

**5 Pentagon**

**6 Hexagon**

**7 Heptagon**

**8 Octagon**

**Regular polygon**

**A polygon is said to be regular if all of its sides are equal. **

**Also all its interior angles are**

**equal. **

**Consequently all exterior angles are also equal.**

**Irregular polygon**

**If all the interior angles are not equal, then the polygon is not regular. It is then known as an**

**irregular polygon.**

**Study the table drawn below:**

**Name of Polygon No of sides No of angles. No of triangles**

**Triangle. 3 3 1**

**Quadrilateral. 4. 4. 2**

**Pentagon 5. 5. 3**

**Hexagon. 6. 6 4**

**Heptagon. 7 7 5**

**Octagon. 8. 8. 6**

**Triangles**

**Triangles can be classified by sides or angles.**

**Draw three triangles on your not book. Name them as ∆PQR, ∆ABC and ∆LMN. With the help of protector measure all the angles the angles and find them:**

**In ∆ABC**

**∠ABC + ∠BCA + ∠CAB = 180°. **

**In ∆PQR**

**∠PQR + ∠QRP + ∠RPQ = 180°**

**In ∆LMN**

**∠LMN + ∠MNL + ∠NLM = 180°**

**Angle Properties of Triangles**

**Here, we observe that in each case, the sum of the measures of three angles of a triangle is 180°.**

**Hence, the sum of the three angles of a triangle is equals to 180°.**

**For Example:**

**1. In a right triangle, if one angle is 50°, find its third angle.**

**Solution:**

**∆ PQR is a right triangle, that is, one angle is right angle.**

**Given, ∠PQR = 90°**

**∠QPR = 50°**

**Therefore, ∠QRP = 180° – (∠Q + ∠ P)**

**= 180° – (90° + 50°)**

**= 180° – 140°**

**∠R = 40°**

**2. Draw a ∆ABC. Measure the length of its three sides. Let the lengths of the three sides be AB = 5 cm, BC = 7 cm, AC = 8 cm. Now add the lengths of any two sides compare this sum with the lengths of the third side.**

**(i) AB + BC = 5 cm + 7 cm = 12 cm**

**Since 12 cm > 8 cm**

**Therefore, (AB + BC) > AC**

**(ii) BC + CA = 7 cm + 8 cm = 15 cm**

**Since 15 cm > 5 cm**

**Therefore, (BC + CA) > AB**

**(iii) CA + AB = 8 cm + 5 cm = 13 cm**

**Since 13 cm > 7 cm**

**Therefore, (CA + AB) > BC**

**two sides of a triangle is greater than the length of the third side.**

**For Example:**

**1. Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm?**

**Solution:**

**The lengths of the sides are 5 cm, 6 cm, 4 cm,**

**(a) 5 cm + 6 cm > 4 cm.**

**(b) 6 cm + 4 cm > 5 cm.**

**(c) 5 cm + 4 cm > 6cm.**

**Hence, a triangle with these sides is possible.**

**We will solve some of the examples of properties of triangle.**

**1. In the triangle, given write the names of its three sides, three angles and three vertices.**

**Solution:**

**Three sides of ∆PQR are: PQ, QR and RP**

**Three angles of ∆PQR are: ∠PQR, ∠QRP and ∠RPQ**

**Three vertices of ∆PQR are: P, Q and R**

**2. Measures of two angles of a triangle are 65° and 40°. Find the measure of its third angle.**

**Solution:**

**Measures of two angles of a ∆ are 65° and 40°**

**Sum of the measures of two angles = 65° + 40° = 105°**

**Sum of all three angles of ∆ = 180°**

**Therefore, measure of the third angle = 180° – 105° = 75°**

**3. Is the construction of a triangle possible in which the lengths of sides are 5 cm, 4 cm and 9 cm?**

**Solution:**

**The lengths of the sides are 5 cm, 4 cm, 9 cm.**

**5 cm + 4 cm = 9 cm.**

**Then the sum of two smaller sides is equal to the third side. But in a triangle, the sum of any two sides should be greater than the third side.**

**Hence, no triangle possible with sides 5 cm, 4 cm and 9 cm.**

**1. Scalene Triangle:**

**A triangle in which all the three sides are unequal in length is called a scalene triangle.**

**Scalene Triangle**

**AC > BC >AB**

**6 cm > 5 cm > 4.5 cm.**

**2. Isosceles Triangle:**

**A triangle in which two of its sides are equal is called isosceles triangle.**

**Isosceles Triangle**

**PQ = PR = 6 cm.**

**3. Equilateral Triangle:**

**A triangle in which have all its three sides equal in length is called an equilateral triangle.**

**Equilateral Triangle**

**LM = MN = NL = 5.5 cm**

**. Classify the triangle into acute triangle, obtuse triangle and right triangle with the following angles:**

**(a) 90°, 45°, 45°**

**(b) 60°, 60°, 60°**

**(c) 80°, 60°, 40°**

**(d) 130°, 40°, 10°**

**(e) 90°, 35°, 55°**

**(f) 92°, 38°, 50°**

**3. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles**

**(a) 6 cm, 3 cm, 5cm.**

**(b) 6 cm, 6 cm, 6 cm.**

**(c) 7 cm, 7 cm, 5 cm.**

**(d) 8 cm, 12 cm, 10 cm.**

**(e) 3 cm, 4 cm, 5 cm.**

**(f) 3.5 cm, 3.5 cm, 4.5 cm.**

**4. Is it possible to have a triangle with the following angles and sides? Give reason in support of your answer.**

**(a) 110°, 60°, 30°**

**(b) 70°, 70°, 70°**

**(c) 80°, 35°, 65°**

**(d) 7 cm, 3 cm, 4 cm.**

**(e) 50°, 50°, 90°**

**(f) 10 cm, 12 cm, 2 cm.**

**5. Find the perimeter of a triangle when its sides are:**

**(a) AB = 7.6 cm, BC = 4.5 cm, CA = 6.3 cm.**

**(b) PQ = 4.00, QR = 3 cm, RP = 5 cm.**

**(c) LM = 4.5 cm, MN = 3.6 cm, NL = 6.2 cm.**

**6. If in a triangle LMN:**

**(a) ∠L = 80°, ∠M = 50°, find ∠N,**

**(b) ∠M = 60°, ∠N = 60°, find ∠L,**

**(c) ∠M = 100°, ∠ N = 30°, find ∠ L,**

**(d) ∠N = 90°, ∠L = 45°, find ∠M.**

**Mention the kind of triangle also.**

**7. The angle of a triangle is in the ratio of 2: 3: 4. Find the measure of each angle of the triangle.**

**8. One of the two equal angles of an isosceles triangle measures 55°. Determine the other angles.**

**9. The perimeter of a triangle is 24 cm. Two of its sides are 8 cm and 9 cm. Find the length of its third side.**

**10. Each side of a ∆ is one third of its perimeter. What kind of triangle is this?**

**11. One of the acute angles of a right triangle is 48°. Find the other acute angle.**

**12. Say whether the following statements are true or false:**

**(a) All the angles of an isosceles triangle are equal.**

**(b) If one angle of a triangle is obtuse, the other two angles must be acute.**

**(c) A right triangle can be equilateral.**

**(d) Equiangular triangle has its three sides also equal.**

**(e) A triangle can have two obtuse angles.**

**Drawing polygons not exceeding octagons**

**1. Acute Angle:**

**An angle whose measure is less than 90° is called an acute angle.**

**Acute Angle**

**∠MON shown in adjoining figure is equal to 60°. So, ∠MON is an acute angle.**

**2. Right Angle:**

**An angle whose measure is 90° is called right angle.**

**Right Angle**

**In the above figure, ∠AOB is a right angle. In this case, we say that the arms OA and OB are perpendicular to each.**

**Therefore, ∠AOB shown in adjoining figure is 90°.**

**So, ∠AOB is a right angle.**

**3. Obtuse Angle:**

**An angle whose measure is greater than 90° but less than 180° is called an obtuse angle.**

**Obtuse Angle**

**6Save**

**∠DOQ shown in the above figure is an obtuse angle.**

**Quadrilaterals**

**These are 4-sided plane shapes. They are rectangles, parallelograms, squares, rhombus,**

**kite and trapezium.**

**Rectangles**

**Opposite sides are equal.**

**Each of the interior angle is 90°.**

**Opposite sides are parallel**

**AB // CD**

**AD // BC**

**The two diagonals are AC and BD. Is AC BD?**

**The two lines of symmetry are MN and ST. Is MN ST?**

**Parallelograms**

**Opposite sides are equal and parallel.**

**A B**

**D C**

**None of the angles is equal to 90°**

**Is diagonal AC BD?**

**How many lines of symmetry has parallelogram ABCD?**

**Squares**

**Opposite sides are equal parallel.**

**A B**

**D C**

**AB CD AD BC**

**All the sides are equal.**

**Each of the interior angle is 90°.**

**Draw the lines of symmetry. How many are they?**

**Is AC BD?**

**Rhombus**

**Opposite sides are equal and parallel. A B**

**C D**

**AB CD and AD BC**

**All the sides are equal.**

**AB CD AD BC**

**None of the angles is equal to 90°.**

**Draw the diagonals AC and BD.**

**Measure AC and BD.**

**Is AC BD?**

**How many lines of symmetry does a rhombus have?**

**Kite**

**Opposite sides are not equal.**

**How many lines of symmetry does a kite have?**

**Name them.**

**Draw the diagonals. How many are they?**

**Name the diagonals.**

**None of the interior angles is equal to 90°.**

**.**

**Trapezium**

**A pair of the opposite sides are parallel.**

**Two of the interior angles may be 90°.**

**How many lines of symmetry does a trapezium have?**

**These are two different types; see fig 1 and fig 2.**

**Draw the diagonals. How many are they?**

**Pentagon**

**A regular pentagon has 5 equal sides**

**and angles.**

**Here AB BC CD DE EA.**

**How many diagonals does a pentagon**

**have?**

**How many lines of symmetry does a**

**pentagon have?**

**Hexagon**

**A regular hexagon has 6 equal sides and**

**angles.**

**How many lines of symmetry does pentagon ABCDEF have?**

**Heptagon**

**A regular heptagon has 7 equal sides and angles.**

**Octagon**

**A regular octagon has 8 equal sides and**

**angles.**

**.**

**Properties of different prisms**

**Properties of a cube**

**It has 6 equal faces. Each face is a square**

**It has 12 straight edges**

**All the edges are equal**

**It has 8 vertices (corners).**

**Properties of a cuboid**

**A cuboid has 6 faces**

**Some faces are either a**

**square or a rectangle**

**It has 12 straight edges**

**It has 8 vertices (corners).**

**Properties of a cylinder**

**A cylinder has 2 plane faces**

**The 2 plane faces are circular**

**It has 1 curved face**

**It has 2 curved edges.**

**Properties of a triangular prism**

**Presentation**

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

**Evaluation** :

**Assignment** :

Prepare for the next lesson by reading about

POLYGON AND PLANE FIGURES