COnstruction of Polygons.pptx

math 7

1. Constructing Polygons and Solving Problems Involving Polygons

2. Triangle a polygon having three sides. can be classified according to angles and sides.

3. A. According to Angles Acute triangle is a triangle whose angles are all acute. Right triangle is a triangle with a right angle. Obtuse triangle is a triangle with an obtuse angle. Equiangular triangle is a triangle with all angles congruent.

4. A. According to Sides Scalene triangle is a triangle with no equal sides. Isosceles triangle is a triangle with two equal sides. Equilateral triangle is a triangle with all sides congruent.

5. Quadrilateral a four-sided polygon. The diagram shows the different kinds of quadrilaterals.

6. A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. A rhombus (plural: rhombi) is a parallelogram with four congruent sides. A rectangle is a parallelogram with four congruent angles. Each interior angle measures 90 O .

7. A s quare is a parallelogram with four congruent sides and four congruent angles. A trapezoid is a quadrilateral with only one pair of opposite sides that are parallel. An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent. A trapezium is a quadrilateral with no pair of opposite sides that are parallel.

8. Constructing Polygons

9. Example 1 Construct △ 𝐴𝐵𝐶 such that 𝐴𝐵̅̅̅̅ = 3 𝑐𝑚, 𝐵𝐶̅̅̅̅ = 5 𝑐𝑚 and 𝐴𝐶̅̅̅̅ = 4 𝑐𝑚 Step 1: Draw 𝐵𝐶̅̅̅̅ of 5 cm using a ruler. Step 2: With 𝐵 as the center and radius of 3 cm (𝐴𝐵̅̅̅̅ = 3 𝑐𝑚), draw an arc using a compass.

10. Example 1 Construct △ 𝐴𝐵𝐶 such that 𝐴𝐵̅̅̅̅ = 3 𝑐𝑚, 𝐵𝐶̅̅̅̅ = 5 𝑐𝑚 and 𝐴𝐶̅̅̅̅ = 4 𝑐𝑚 Step 3: With 𝐶 as the center and radius of 4 cm (𝐴𝐵̅̅̅̅ = 4 𝑐𝑚), draw an arc to cut the previous at 𝐴. Step 4: Draw a segment 𝐴𝐵̅̅̅̅ and 𝐴𝐶̅̅̅̅̅ using a ruler to get △ 𝐴𝐵𝐶

11. Example 2: Construct a square having 4 cm as length of each side. Step 1: Draw 𝐴𝐵̅̅̅̅ of length 4 cm. Extend 𝐴𝐵̅̅̅̅ to the right. Step 2: Draw an arc on each side 𝐵 using any compass width. Label these 𝑀 and 𝑁.

12. Step 3: With the compass on 𝑁 and any width, draw an arc above 𝐵. Step 4: Without changing the width, draw an arc using point 𝑀 and name it 𝑂. Example 2: Construct a square having 4 cm as length of each side.

13. Step 5: Draw a line perpendicular from 𝐵 to 𝑂. Step 6: Set the compass on 𝐴 and set its width to the length of 𝐴𝐵 which is 4 cm. Example 2: Construct a square having 4 cm as length of each side.

14. Step 7: Using point A make an arc above 𝐴 and using point 𝐵 make an arc above 𝐵, label it 𝐶. Example 2: Construct a square having 4 cm as length of each side.

15. Step 8: Move the compass to 𝐶 and make an arc on the left of 𝐶, then label it 𝐷 Step 9: Connect points C and D; points D and A. Example 2: Construct a square having 4 cm as length of each side.

16. CONSTRUCT A REGULAR POLYGON

17. Construct a regular pentagon with 6 cm as the length of each side. Step 1: Draw 𝐴𝐵̅̅̅̅ with length 6 cm.

18. Construct a regular pentagon with 6 cm as the length of each side. Step 2: Draw 108º angles at 𝐴 and 𝐵.

19. Construct a regular pentagon with 6 cm as the length of each side. Step 3: Mark 6 cm on these sides and label 𝐸 and 𝐶.

20. Construct a regular pentagon with 6 cm as the length of each side. Step 4: Draw 6 cm arcs using 𝐸 and 𝐶 as the centers. Mark the point as 𝐷.

21. Construct a regular pentagon with 6 cm as the length of each side. Step 5: Connect the points 𝐷 and 𝐸; 𝐶 and 𝐷.

22. Triangle Construct a scalene triangle such that 𝐷𝐸̅̅̅̅ = 3 𝑐𝑚, 𝐸𝐹̅̅̅̅ = 7 𝑐𝑚 and 𝐷𝐹̅̅̅̅ = 5 𝑐𝑚. Label it △ 𝐷𝐸𝐹.

23. Square and Rectangle Construct a square having 8 cm as the length of each side Construct a rectangle having 3 cm as the length and 2 cm as the width by following the steps given below. Step 1: Draw 𝐴𝐵̅̅̅̅ of 3 cm. Step 2: Construct 90⁰ angle at 𝐴 and 𝐵. Step 3: Draw arcs of radius 2 cm from 𝐴 and 𝐵 to cut the rays respectively at 𝐷 and 𝐶. Step 4: Connect points 𝐶 and 𝐷 to obtain ▭𝐴𝐵𝐶𝐷.

24. Regular Pentagon and Hexagon Construct a regular pentagon given 4 cm as the length of each side. Construct a regular hexagon given points 𝐴,𝐵, 𝐶,𝐷,𝐸 𝑎𝑛𝑑 𝐹 having 4 cm as the length of each side.

25. Read and construct the following: 1. Construct a square having 5 cm as the length of each side. 2. Construct a regular pentagon given 6 cm as the length of each side. 3. Construct a regular hexagon given points H,O, R,S,E 𝑎𝑛𝑑 U having 4 cm as the length of each side. 4. Construct △ SME such that SM̅̅̅̅ = 5 𝑐𝑚,ME̅̅̅̅ = 8 𝑐𝑚 and SE̅̅̅̅ = 7 𝑐𝑚

26. Look at your surroundings and observe everything. In a long bond paper, draw an object that shows the shape of: 1. Triangle 2. Square 3. Rectangle 4. Regular pentagon 5. Regular hexagon. Make it attractive and creative

27. Construct a Square

28. Construct a Rectangle

29. Construct a Pentagon

30. Construct a Pentagon

31. On a separate sheet of paper, match the correct answer in column B. Write only the letter of your answer in the space provided. Column A Column B 1. Find the sum of the measures of the a. 900 vertex angles for octagon. b. 9 2. Find the sum of the measures of the c. 1,080 vertex angles for hexagon d. 13 3. Find the sum of the measures of the e. 720 vertex angles for heptagon f. 1,260 4. Find the number of sides of the regular polygon when the sum of the measures of the vertex angle is 1,2600 5. Find the number of sides of the regular polygon when the sum of the measures of the vertex angle is 1,980

32. Construct the following in a separate sheet of paper. 1. A triangle whose sides have lengths 2.5cm and 3cm with an included angle of 30º. 2. A rectangle whose length is equal to 3cm and width equal to 2.5cm. 3. A regular pentagon whose side equal to 2.7cm. 4. A regular hexagon whose sides equal to 3.5cm